Pierre Laumonerie
email: jaumonerie.pierre@hotmail.fr

Meagan E Tibbo

• Gregoire Laumond

Dominique Barbier

Pauline Assemat

Pascal Swider

Franck Accadbled

Does a combined screw and dowel construct improve tibial fixation during anterior cruciate ligament reconstruction?

Keywords: Anterior cruciate ligament, Tibial fixation, lnterference screw, Biomechanical strength Abbreviations ACL Anterior cruciate ligament BMD Bone mineral density

Purpose The aims of the present study were to compare the biomechanical properties of tibial fixation in hamstring graft ACL reconstruction using interference screw and a novel combination interference screw and dowel construct. Material and Methods We compared the fixation of 30 (2-and 4-stranded gracilis and semitendinosis tendons) in 15 fresh-frozen porcine tibiae with a biocomposite resorbable interference screw (Group 1) and a screw and dowel construct (Group 2). Each graft was subjected to load-to-failure testing (50 mm/min) to determine maximum load, displacement at failure and pullout strength. Results There were no significant differences between the biomechanical properties of the constructs. Multivariate analysis demonstrated that combination constructs (� = 140.20, p = 0.043), screw diameter (� = 185, p = 0.006) and 4strand grafts (� = 51, p = 0.050) were associated with a significant increase in Joad at failure. Larger screw diameter was associated with increased construct stiffness (� = 20.15, p = 0.020). Conclusion The screw and dowel construct led to significantly increased fixation properties compared to interference screws alone in a porcine model. Increased screw diameter and utilization of 4-strand ACL grafts also led to improvement in load-to-failure of the construct. However, this is an in vitro study and additional investigations are needed to determine whether the results are reproducible in vivo. Level of evidence Level V; Biomechanical study.

Introduction

Anterior cruciate ligament (ACL) reconstruction is one of the most commonly performed orthopedic procedures, with more than 100,000 being performed annually in the USA [START_REF] Bach Br | Revision anterior cruciate ligament surgery[END_REF]. Stable graft fixation is critical during the early rehabili tation phase of anterior cruciate ligament (ACL) reconstruc tion to avoid graft elongation and failure. The tibial fixation site is mechanically the weakest point, due to the reduced bone minerai density (BMD) of the tibial metaphysis [START_REF] Brand | Interference screw fixation strength of a quadrupled hamstring tendon graft is directly related to bone mineral density and insertion torque[END_REF]29]. Additional hypotheses suggest that the angle at which the forces are applied to the tibial graft also contributes to decreased pullout strength [START_REF] Brand | Interference screw fixation strength of a quadrupled hamstring tendon graft is directly related to bone mineral density and insertion torque[END_REF][START_REF] Ferretti | Evolgate fixation of doubled flexor graft in anterior cruciate ligament reconstruction: biomechanical evaluation with cyclic loading[END_REF].

Evidence-based selection of a tibial fixation construct remains challenging due to limited clinical data, as well as variability in outcomes reporting and surgical technique. To date, interference screw fixation is one of the most commonly utilized fixation techniques for soft tissue grafts [START_REF] Hamner | Hamstring tendon grafts for reconstruction of the anterior cruciate ligament: biomechanical evaluation of the use of multiple strands and tensioning techniques[END_REF]. However, there is no consensus with respect to the clinical superiority of one cortical suspension device compared to another for ACL reconstruction. Those that have compared various methods of tibial fixation have demonstrated no differences in clinical outcomes [START_REF] Han | Intratunnel versus extratunnel fixation of hamstring autograft for anterior cruciate ligament reconstruction[END_REF][START_REF] Lubowitz | All-inside anterior cruciate ligament graft-link technique: second-generation, noincision anterior cruciate ligament reconstruction[END_REF].

Depending on the series, interference screws [START_REF] Ferretti | Evolgate fixation of doubled flexor graft in anterior cruciate ligament reconstruction: biomechanical evaluation with cyclic loading[END_REF], screw and washer fixation [START_REF] Giurea | Comparative pull-out and cyclic-loading strength tests of anchorage of hamstring tendon grafts in anterior cruciate ligament reconstruction[END_REF]24], stirrups [START_REF] Giurea | Comparative pull-out and cyclic-loading strength tests of anchorage of hamstring tendon grafts in anterior cruciate ligament reconstruction[END_REF], suspension button [25] or a combination of these [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF] have all been linked to superior biomechanical tibial fixation. However, the current literature lacks a robust biomechanical comparison of interference screws and combination of screw and dowel devices with a similar insertion technique [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF]. The aims of the present study were to compare the biomechanical properties of tibial fixation in hamstringgraft ACL reconstruction using interference screw and a novel combination interference screw and dowel construct (Amplitude, France; Biomatlante, France). Intratunnel tibial fixation was assessed via tensile load-to-failure. We hypothesized that the combined screw and dowel construct would provide improved tibial fixation properties compared to screws alone in a porcine model.

Methods

Two soft tissue tibial tunnel fixation devices were biomechanically evaluated utilizing load-to-failure testing. We assessed a biocomposite resorbable interference screw OSTEOTWIN (Biomalante, France) and a screw and dowel construct ECLIPSE BCP (Biomalante, France) (Fig. 1).

Specimen preparation

Testing was performed on 15 fresh-frozen mature porcine tibias (Lyon, France). The porcine model was selected because prior studies have reported similar biomechanical properties to that of the young adult human knee [26,31]. A total of 30 fresh cadaveric gracilis and semitendinosus tendons were harvested from 15 cadavers at our university's anatomy laboratory (Paul Sabatier University, Toulouse, France). Specimens were stored at -20 °C. Two-(n = 12) and four (n = 15)-strand grafts were created and adjusted to 7, 8 or 9 mm in diameter with a graft sizing block. Those that were smaller than 7 mm were excluded, and those that were larger than 9 mm were trimmed in line with the fiber orientation. The 27 grafts were assigned to 2 groups; interference screw fixation only (Group 1, n = 12)), and screw and dowel fixation (Group 2, n = 15).

Description of fixation methods

All grafts were inserted by a single surgeon (GL) according to the manufacturers' specifications. Screw diameter and the corresponding dowel and instrumentation size used are reported in Table 1. For each tibia, two tunnels were prepared using a tibial drill guide set at a 45° angle on either side of the tibial tuberosity. The guide pin was advanced from the anteromedial proximal tibia through the footprint of the native ACL. The tibial tunnels were reamed to a diameter of 7, 8 or 9 mm (Table 1); the diameter of the reamer was selected based on the graft diameter (line-to-line fit). The graft was manually pulled through the tibial tunnel from distal to proximal until > 50 mm of the graft had advanced through the proximal aperture. During the entirety of the procedure, tension was manually applied to the graft distally and in line with the tunnel. For screw-only fixation, the tibial tunnel was tapped to allow insertion of the interference screw until it was flush with the cortical bone. For the combined dowel and screw fixation, a dilator was used to adjust the tunnel, and a corresponding sheath was introduced between the graft and the tibial tunnel. Finally, the screw was inserted flush with the cortical bone. The size of the screw was selected to match the diameter of the tunnel (7 × 25 mm, 8 × 25 mm or 9 × 25 mm).

Experimental apparatus

All screws were inserted with a torque meter (Chatillon® DFS2-R-ND with digital force sensor STS-0100, Ametek, Largo, Flo. the USA) in order to allow recording of the torque after insertion to 1/4, 1/2, 3/4, and at the completion of insertion. All grafts/fixation systems were subject to loadto-failure testing utilizing a dynamic load cell (Instron 3366; Instron Systems, Norwood, MA, the USA). The proximal 50 mm portion of the graft was looped over a 4.5 mm diameter stainless bar and mounted onto the dynamic load cell. After the application of a 10 N preload, the proximal tibia is held in place without the need for any further modification. This mounting system allowed the axis of the tibial bone tunnels to be collinear with the applied load (Fig. 2).

Load-to-failure tests

Parameters for tensile load-to-failure testing protocol were selected after the literature search and synthesis of common parameters from the various protocols [START_REF] Hamada | Single-versus bi-socket anterior cruciate ligament reconstruction using autogenous multiple-stranded hamstring tendons with endoButton femoral fixation: A prospective study[END_REF]30,32].

As a result, the graft was first preloaded with a constant 10-N tensile force to allow for system accommodation [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF]. After the preloading protocol, grafts were further displaced at 50 mm/min until failure [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF] to simulate a sudden overload event at the knee. Biomechanical parameters including load at failure (N), displacement at failure (mm) and pullout stiffness (N/mm) were measured. Displacement at failure was measured as the total elongation at ultimate failure and accounted for tendon elongation, graft slippage or tearing and device pullout. Stiffness was calculated from the same linear portion of the load-elongation curves from the load-to-failure raw data. The mechanism Fig. 2 Biomechanical testing setup utilizing a dynamic load cell device (Instron 3366; Instron Systems, Norwood, MA, USA), which allowed for the force vector to be applied in line with the tibial tunnel on the four-strand graft fixed with screw and sheath construct (e.g., grafts slippage, graft tear, device pullout or ligaments peeled off from their insertions) and the site of failure were also observed and recorded.

Statistical analysis

Descriptive statistics (mean with standard deviation for continuous variables and frequencies with proportions for categorical data) were used to summarize recorded variables. Wilcoxon rank sum (nonparametric test) tests were used to assess univariate differences between screw-only and combined screw and dowel groups. In order to discern the effect of the device, the screw diameter, number of graft strands, displacement at failure and stiffness were corrected for in the multivariable linear regression model. P values less than 0.05 were considered statistically significant. Statistical analysis was conducted using R (version 3.3.2, R Core Team 2013. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria).

Results

Results from the load-to-failure testing and p values for univariate comparisons between Groups 1 and 2 are reported in Table 2. The mean ultimate load at failure and stiffness were 515 N (SD 122.98) and 70.5 N/mm (SD 22.16) with screws and dowels, respectively. The mean ultimate load at failure and stiffness were 336.5 N (SD 153.24) and 55.1 N/mm (SD 20.18) with screws alone. The univariate comparisons revealed no significant difference between screws alone and combined devices. Multivariable analysis (Table 3) demonstrated that the use of combined fixation with screws and dowels (β = 140.20 (95% CI 5 to 297), p = 0.043), screw diameter (β = 185.05 (95% CI 61 to 309), p = 0.006) and 4-strand grafts (β = 51.00 (95% CI 7 to 187), p = 0.050) was associated with a significant increasing in ultimate load at failure. The increased screw diameter was also associated with increased construct stiffness (β = 20.15 (95% CI 4 to 37), p = 0.020).

There were no differences between devices with respect to the mode of failure. Recorded failure modes were graft

Discussion

Based on the results of the present study, fixation obtained using a screw and dowel construct led to a significant increase in biomechanical properties compared with interference screws alone, in a porcine ACL reconstruction model. Multivariate analyses in the present study showed that the addition of a dowel to the interference screw was associated with a significant increase in ultimate load-to-failure (β = 140, p = 0.043) and stiffness (β = 20, p = 0.020). Combination devices were hypothesized to improve biomechanical properties by separating limbs of the graft, ensuring concentric placement of the screw, and providing homogeneous friction between the tendon and tibial metaphyseal bone [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF][START_REF] Ferretti | Evolgate fixation of doubled flexor graft in anterior cruciate ligament reconstruction: biomechanical evaluation with cyclic loading[END_REF]. Combination fixation could also improve fixation characteristics by increasing radial force and compression on the graft against the tunnel wall [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF][START_REF] Ferretti | Evolgate fixation of doubled flexor graft in anterior cruciate ligament reconstruction: biomechanical evaluation with cyclic loading[END_REF]. While Kousa et al. [START_REF] Kousa | The fixation strength of six hamstring tendon graft fixation devices in anterior cruciate ligament reconstruction. Part II: tibial site[END_REF] found that the combination device provided significantly higher ultimate failure strength and decreased displacement compared with the other devices (i.e., interference screws and extracortical devices), Aga et al.'s [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF] results showed that the combination of a screw and dowel did not consistently result in improved fixation characteristics compared to interference screw fixation alone. In fact, the authors [START_REF] Aga | Biomechanical comparison of interference screws and combination screw and sheath devices for soft tissue anterior cruciate ligament reconstruction on the tibial side[END_REF] reported inferior fixation among combination devices. We posited that differences in insertion technique [31,32], screw length [START_REF] Butler | Optimal graft fixationthe effect of gap size and screw size on bone plug fixation in ACL reconstruction[END_REF]32], surgical technique [35] and number of graft strands [START_REF] Gadikota | Biomechanical comparison of single-tunneldouble-bundle and single-bundle anterior cruciate ligament reconstructions[END_REF][START_REF] Hamada | Single-versus bi-socket anterior cruciate ligament reconstruction using autogenous multiple-stranded hamstring tendons with endoButton femoral fixation: A prospective study[END_REF] likely contributed to the significant variability of biomechanical properties described in the literature.

The screws and dowels were inserted according to the manufacturers' recommendations. We performed tunnel dilations in addition to simple tunnel reaming to create impaction of the surrounding cancellous bone and increase tunnel wall bone volume, in an effort to increase fixation strength [START_REF] Gokce | Does bone impaction technique reduce tunnel enlargement in ACL reconstruction?[END_REF]. Although Cain et al. [START_REF] Cain | Effect of tibial tunnel dilation on pullout strength of semitendinosus-gracilis graft in anterior cruciate ligament reconstruction[END_REF] demonstrated a beneficial effect of dilation on fixation properties in cadaveric bones, Rittmeister et al. [28] did not report any significant improvement in young human cadaveric specimens. According to Dunkin et al. [START_REF] Dunkin | Soft tissue tendon graft fixation in serially dilated or extraction-drilled tibial tunnels: a porcine model study using highresolution quantitative computerized tomography[END_REF], the reduced effect of dilatation on fixation in younger patients' tibiae is likely associated with higher bone mineral density and may explain the conflicting results in the literature.

Our data suggest that the 4-stranded grafts (β = 51, p = 0.05) had significantly higher ultimate load-to-failure compared to 2-stranded grafts. Hamner et al. [START_REF] Hamner | Hamstring tendon grafts for reconstruction of the anterior cruciate ligament: biomechanical evaluation of the use of multiple strands and tensioning techniques[END_REF] demonstrated that there was a strong positive linear correlation between maximum failure load and the cross-sectional area for 1-strand, and equally tensioned 2-and 4-strand hamstring tendon grafts. Boniello et al. [START_REF] Boniello | Impact of Hamstring Graft Diameter on Tendon Strength: A Biomechanical Study[END_REF] reported similar findings. However, Hamner et al. [START_REF] Hamner | Hamstring tendon grafts for reconstruction of the anterior cruciate ligament: biomechanical evaluation of the use of multiple strands and tensioning techniques[END_REF] also highlighted that applying unequal tension graft strands led to significantly lower failure loads for a given cross-sectional area. The authors of the aforementioned studies [START_REF] Boniello | Impact of Hamstring Graft Diameter on Tendon Strength: A Biomechanical Study[END_REF][START_REF] Hamner | Hamstring tendon grafts for reconstruction of the anterior cruciate ligament: biomechanical evaluation of the use of multiple strands and tensioning techniques[END_REF] posited that the lower revision rates associated with larger diameter hamstring tendon grafts were due to the fact that these grafts are stronger. While most published biomechanical studies compared various devices using 4-stranded grafts, the influence of the number of graft strands on tibial fixation could explain the lack of significant differences between fixation devices in our study and others.

The choice of the screw diameter employed in this study was determined by the tunnel diameter, which was in turn dictated by the size of the prepared graft (Table 1). We found that increased screw diameter was correlated with an increased ultimate load-to-failure. However, results in the literature are mixed with respect to the effect of screw diameter and length on fixation properties. A biomechanical study by Weiler et al. [32] analyzed the effect of varying screw diameter as well as lengths on graft fixation. Their results suggested that screw length had a greater impact on fixation strength than screw diameter. They did, however, recommend oversizing the screw by 1 mm (with respect to the tunnel size) due to concern for graft slippage. Two studies evaluating graft slippage showed similar findings with no difference between 7-and 9-mm screws [31].

Limitations

The present study is not without limitation. The results achieved in an in vitro biomechanical animal model cannot be directly transferred to a clinical setting. Second, we did not perform cyclic load-to-failure testing which would likely provide more physiologically relevant data. Third, the screws and dowels utilized in the present study were resorbable biocomposite and the extent to which the biomechanical properties degrade over time was not assessed. And lastly, differences in biomechanical properties may also have been influenced by testing setup. Woo et al. [33] found that specimen age and graft orientation had a significant influence on the structural properties of the human ACL. Age-related decreases in ACL linear stiffness, ultimate load-to-failure and energy absorbed at failure have also been demonstrated. Furthermore, a higher percentage of ligament insertional avulsions have been reported among ACLs tested in the tibial orientation (i.e., tensile load applied along the axis of the ACL in the line with the tibial insertion site) (Fig. 2) compared to the anatomic orientation (i.e., Tensile load applied along the axis of the ACL, while the normal anatomical angle of the ACL insertion to the bone was preserved) [33]. These data may explain the large decrease in ACL fixation properties in the present series compared to studies using young human tissue tested in an anatomic orientation [24]. These data further highlight the importance of a constant test setup in an effort to reduce the impact of confound orders on the biomechanical model. In the same vein, future studies should utilize consistent insertion technique and tissues with the consistent or measurable internal by mechanical properties in an effort to isolate the effect of a single fixation modality.

Conclusions

In conclusion, the addition of a dowel improves biomechanical properties of tibial fixation of hamstring grafts in a porcine ACL reconstruction model. Larger diameter graft also improved fixation properties including ultimate load-to-failure.

Fig. 1

 1 Fig. 1 Tibial fixation devices included: a a biocomposite resorbable interference screw OSTEOTWIN (Biomalante, France) and b a sheath ECLIPSE BCP (Biomalante, France)

Table 1

 1 Anterior cruciate ligament reconstruction tunnel, implant and instrumentation sizes

	Tunnel	Implant*		Instrumentation
	diameter	Screw	Dowel size	Dilator	Introducer
		diameter
	7	7	7/8	7/8	7/8
	8	8	7/8	7/8	7/8
	9	9	9/10	9/10	9/10
	All dimensions are listed in millimeters
	*Constant length 25 mm

Table 2

 2 Results of load-to-failure testing and p values from univariate comparisons between devicesOve., Overall, D.S., and Q.S., Double strand, and quadruple strand *Comparisons between the overall result of screws alone and combined devices (screws and dowels)

	Variable		Screws			Screws and dowels	p value*
			Ove	D.S	Q.S	Ove	D.S	Q.S
			n = 12	n = 6	n = 6	n = 15	n = 6	n = 9
	Torque tightening Nm, mean (SD)
	1/4		0.66 (0.21)	0.58 (0.20)	0.75 (0.21) 0.87 (0.21)	0.813 (0.31) 0.95 (0.04)	0.35
	2/4		0.85 (0.22)	0.89 (0.25)	0.80 (0.19) 1.11 (0.22)	1.01 (0.43)	1.18 (0.16)	0.52
	3/4		1.07 (0.36)	1.08 (0.32)	1.06 (0.46) 1.53 (0.36)	1.43 (0.44)	1.40 (0.34)	0.52
	4/4		1.09 (0.37)	1.35 (0.37)	0.84 (0.09) 1.64 (0.37)	1.81 (0.49)	1.64 (0.65)	0.53
	Ultimate load at failure N, mean (SD)	336.5 (153.24) 260 (72.21) 413 (103)	515 (122.98) 440.83 (134) 565 (101.08) 0.32
	Displacement at failure mm, mean (SD) 4.16 (3.2)	5.72 (1.90)	2.61 (1.44) 3.33 (1.24)	3.65 (1.26)	3.08 (1.65)	0.26
	Stiffness N/mm, mean (SD)		55.1 (20.18)	52.6 (14.10) 57.6 (20.1) 70.46 (22.16) 65.9 (19.11) 73.5 (21.94) 0.51
	Table 3 Results of multivariable linear regression	Variables	Ultimate load at failure	Displacement at failure	Stiffness
	analysis			β-Coef (95% IC) p value β-Coef (95% IC)		p value β-Coef (95% IC) p value
		Devices
		Screw	Reference		Reference		Reference
		Screw and dowel 140 (5 to 297)	0.043	-0.4 (-2.71 to 1.95) 0.74	20.2 (4 to 37)	0.020
		Screw diameter 185 (61 to 309) 0.006	-0.5 (-2.7 to 1.7)	0.63	6.4 (-12 to 24) 0.465
		No. of graft strands
		Double	Reference		Reference		Reference
		Quadruple	51 (7 to 187)	0.050	-1.5 (-3.9 to 0.84) 0.19	0.3 (-16 to 17) 0.970
		p values in bold are statistically significant

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Funding This research received no specific grant from any funding agency in the public, commercial or not for profit sectors.

Disclosures

Author contribution PL contributed to data analysis and interpretation, critical revisions, manuscript review, statistical analysis. MET was involved in data analysis and interpretation, critical revisions, manuscript review. GL and DB contributed to data acquisition. PA was involved in data acquisition, study design, data analysis and interpretation, critical revisions, manuscript review, administration, technical and material support. PS and FA contributed to study design, data analysis and interpretation, critical revisions, manuscript review, administration, technical and material support, study supervision.

Conflict of interest

The authors report no conflicts of interest with respect the materials or methods used in this study or the findings specified herein.


Olivier Rozenbaum
email: rozenbaum@cnrs-orleans.fr

D De Sousa Meneses

Patrick Echegut
email: echegut@cnrs-orleans.fr

Domingos De

Sousa Meneses

Texture and porosity effects on the thermal radiative behavior of alumina ceramics

Keywords: ceramics, texture, emissivity spectra, infrared spectroscopy, high temperature

Thermal and optical properties of ceramics are dependent on radiation scattering and cannot be determined by the only knowledge of their chemical composition as for single crystals. In this paper, we investigate extrinsic effects such as roughness, porosity and texture on spectral emissivity of alumina ceramics. Roughness effects have an influence mainly in the opaque zone; an important porosity dependence and the presence of a critical porosity threshold were also pointed out in the semi-transparent zone. Furthermore, it was shown that two ceramics with similar total porosity but with different textures possess radically different emissivities, showing that grain size, pore size and spatial repartition of the grains is also crucial for the comprehension of the ceramics thermal properties.

1-Introduction

A precise characterization of the thermal radiation heat transfer efficiency of structural materials is mandatory to design and optimize devices working at high temperature such as glass making furnaces or thermal shields. To determine these properties, a direct measurement of the spectral emissivity is a must as shown in the available literature on this subject (e.g. [1][2]). The optical and radiative properties of single crystals and non porous materials are relatively well-known and completely defined by the only knowledge of intrinsic parameters such as the complex refractive index and the thickness of the material [3][START_REF] Siegel | Thermal radiation of heat transfer[END_REF][START_REF] Rozenbaum | [END_REF]. Nevertheless, these properties are modified by extrinsic parameters in the case of porous materials such as ceramics. Some authors [6][7][8][9][10][11][12] pointed out the effect of the structure of ceramics, the roughness, the porosity, the grain and pore size, the birefringence and the role of impurities within the grain boundaries. However, as shown by Grimm et al. [8], Budworth [13] and Peelen [6], the effect of the birefringence is negligible compared to the pore size effect. Also, the only knowledge of the chemical formula of a material is not sufficient to have a perfect understanding of the associated ceramics emissivity.

In this paper, it is shown how some extrinsic contributions act on the spectral emissivity of alumina ceramics. All the reported measurements were performed with a set-up [2] that enables to obtain accurate emissivity spectra of semitransparent porous and non porous materials. After a brief description of the set-up and the studied ceramics, the influences of the porosity, the texture effect on the radiative properties of alumina ceramics will be exposed and discussed.

Material and method

Spectral emissivity measurement

The apparatus, previously described in details [2], consists in a FTIR Bruker IFS 113v spectrometer which was enhanced with an external optical device that allows the measurement of infrared fluxes emitted by a sample and a black body furnace for identical geometrical conditions. To achieve very high temperatures (2500 K) and avoid parasite flux due to hot closure confinement, a CO 2 laser heating was chosen. The particular design of the heating configuration enables to obtain a quasi homogeneous temperature on the measured sample area. The sample temperature was determined at a particular wavelength called the "Christiansen point" [1][2]. Indeed, at this wavelength polar dielectric materials such as oxide materials behave like a blackbody (ε=1). This characteristic point suffers little change with temperature and was quasi independent on the texture and the material roughness. Hence, the temperature determination can then be obtained by using the spectrometer as a pyrometer at the Christiansen wavenumber. For alumina materials, the Christiansen wavelength is near 1030 cm -1 .

For stability reasons and better precision, the temperature of the blackbody furnace was maintained at 1673 K. So, the spectral emissivity of a sample at temperature T was calculated by the following expression [14]: were the interferograms recorded respectively for the sample, the blackbody reference and the room temperature parasite flux, S P , BB P and RT P were the calculated Planck's function at the sample temperature, the blackbody furnace, and a blackbody at room temperature.

Materials

The choice of several alumina ceramics with perfectly controlled characteristics was imposed by several constraints. The first one was the necessity to obtain enough emitted energy in the mid infrared range or, in other words, the necessity to select a material whose texture does not evolve with temperature, allowing high temperature measurements. Another one was the fact that the samples must be good absorbers at the CO 2 laser frequency to be efficiency heated.

Two sets of high purity alumina ceramics covering a large range of porosity and with a fixed texture were obtained from an industrial supplier (Desmarquest) and from a French public laboratory (CEA-CEREM). Hereafter the samples were labeled by the following nomenclature: Compound(Origin)-Porosity. So, a CEA's alumina ceramic with a porosity of X % will be named Al(C)-X. For the ceramics made by Desmarquest, the letter D was used for the classical process of fabrication and D' for one particular ceramic. Indeed, most of the alumina ceramics elaborated by Desmarquest resulted from a classical industrial process from a biomedical powder (alumina α, purity 99.9 %). All these ceramics were made from powders with the same grain diameter (approximately 0.5 µm) and different porosities were obtained by using different sintering temperatures (Tableau 1). Except for one particular ceramic noted Al(D')-23.2 that was made from a bimodal grain distribution in order to study the effect of the texture. The second set of ceramics came from the CEA-CEREM laboratory and was made from an α alumina powder with purity higher than 99.99 %. The powder was calcined at 1273 K, to obtained larger grains and then crushed. The resulting clusters was then sieved at 400

µm and pressed at 1500 bars with an isostatic press to form alumina rods. Finally, the different porosities were obtained by using different sintering temperatures (Tableau 1). As the only varying parameter during the elaboration process was the sintering temperature, the resulting ceramics possessed analogous texture and differ only by their porosity. Indeed, the observation of different ceramics fractures by Scanning Electron Microscopy (SEM) was carried out to control the sintering effect and to obtain the average grain size and morphology (Figure 1, Figure 2, Figure 3, and table 1). For porosities (measured by geometrical measurements and helium pycnometry) lying between 3.8 and 29.2 % (CEA's samples), all the ceramics exhibits analogous morphology and spatial arrangement. The only significant change was the mean grain size that slightly increases along with the higher sintering temperatures. Furthermore, image analysis on Desmarquest ceramics (Al(D)-0.6 and Al(D)-3.5) showed that these materials have roughly similar grain size and spatial repartition. These sets of samples were then appropriate to study the influence of the porosity on the spectral emissivity.

In contrast, the bimodal grain distribution of the Al(D')-23.2 sample belonged to the 5-50 µm range. Mercury intrusion porosimetry analysis showed that the mean pore size of this sample was 40 times as high as the mean pore size of the other ceramics (not shown here). The large pore size was explained by the presence of large grains (50 µm) that originates macropores.

Results

For the study of the porosity effect all the emissivity spectra were acquired on one millimeter thick polished samples at 1350 K in order to stay below the sintering temperature and retain the initial texture of the most porous ceramic. To ensure that the spectra obtained on a single sample were self-averaged, several measurements on different samples with identical texture and equivalent porosity (table 1) were performed. For the sake of clarity, only sets of the more representative samples were kept in the following figures.

In the 400-1300 cm -1 range (Figure 4), alumina ceramics were opaque (phonon zone) and the optical properties were only due to the material surface. For higher wavelengths, i.e. between 1300 and 2500 cm -1 , the absorption coefficient decreases and the material becomes semitransparent. For the most porous samples, broad bands appeared in the emissivity spectra between 2600 and 4000 cm -1 (Figure 4) and were not the only consequence of the porosity.

The microscopic origin of these bands comes from the hydroxyls groups and trapped water molecules. These bands did not appear in dense ceramics because of their closed porosity and the fact that during their elaboration they were sintered at higher temperatures by comparison with the most porous ones. Without these contributions, i.e. above 4000 cm -1 , the absorption coefficient becomes intrinsically sufficiently weak to consider the material as transparent and the emissivity negligible [START_REF] Rozenbaum | [END_REF].

The porosity effect was observed by the juxtaposition of the spectral emissivities of the CEA's samples (Al(C)-3.8 to Al(C)-29.2) and the Demarquest's samples (Figure 4). A rapid overview on this figure showed two different aspects of the porosity effect: a frequency shift of the transmissivity edge by comparing it to those of the single crystal, and an enhancement of the emissivity in the phonon wavenumber range (opaque zone).

Roughness effect in the opaque zone

The porosity dependence on the spectral emissivity in the phonon range was reported in Figure 5. With the porosity increase, a strengthening of the surface scattering was noticed which results in a progressive weakening of the reflection bands, and then an enhancement of the emissivity. Besides, in addition to these progressive modifications, the band shapes were markedly modified in comparison with those of the single crystal but the bands shapes did not evolve significantly with the increase in porosity between 500 and 900 cm -1 . Several authors [10,[15][16][17][18][19] showed that the band shape of the spectral emissivity was dependent on the grain size and the grain shape constituting the surface of the sample. Several types of behaviors appeared according to the particle size and the value of the absorption coefficient K (e.g. [16]). For high values of absorption coefficient (opaque zone), these authors showed that the particle size decrease induced a reflectivity drop fall leading to an increase of emissivity.

Furthermore, Anderson and Ribbing [20] have pointed out that the spectral emissivity was also particle shape dependent. Following their work, a distortion of the reflection band, near the longitudinal optic mode wavenumber (850 cm -1 for alumina), was due to surface defects with spherical shape. This general trend was in accordance with the bump localized in the emissive spectra, around 720 cm -1 (Figure 5). Indeed, SEM images obtained on the ceramics of CEA show that the grains were polyhedrons with quasi spherical shape (Figure 2).

Porosity effect

The porosity dependence on the spectral emissivity in the semitransparent region was reported in Figure 6 and the emissivity evolution with respect to the porosity was visualized for three wavenumbers in Figure 7. In this spectral range, ceramics emissivities were always higher than those of the single crystal. Furthermore, for small values of total porosity (0-5 % range) the emissivity increased as the ceramics became more and more porous. To our knowledge, few results related to this subject were published [6-8, 11-12, 21-23]. Some authors [19,24] determined by transmissivity measurements that, in the semitransparent region, the radiation scattering inside ceramics was mainly due to the pores. Scattering by grain interfaces in weak anisotropic material such as dielectric oxides in the semitransparent zone was always weak in comparison with the previous mode. With transmissivity measurements made on dense ceramics (<2% of porosity) Grimm [8] showed that a density decrease i.e. a porosity increase, strengthens radiation scattering (backscattering) and lowers the sample transmissivity (inducing an emissivity increase). These results were consistent with the present work and explain the observed phenomenon. Besides, for higher total porosity, a change of behavior was observed since the emissivity decreases continuously (Figure 7). This result shows the existence of a critical porosity for which the emissivity reaches the highest value in the semitransparent zone for this type of texture.

Texture influence

As for porosity, spatial repartition, grain size and pores size, parameters that we call texture, influence largely the radiative properties of a material. This point can be brought to the fore by a comparison between the Al(D')-23.2 and the Al(C)-20.6 samples that possess similar total porosity but very different textures as showed in Figure 2 and Figure 3. The main modifications between the spectral emissivity spectra of these two samples (Figure 8) occur in the semitransparent zone. Unlike the other previously studied ceramics, the Al(D')-23.2 ceramic have a much lower emissivity than the single crystal between 1300 and 1800 cm -1 and the spectral emissivity of this sample was radically different from the Al(C)-20.6 emissivity spectra. For higher wavelengths, the emissivity increases to become higher than those of the single crystal and tends to those of the Al(C)-20.6 sample in the transparent zone.

The only total porosity knowledge is then not sufficient to predict the radiative behavior of porous materials and confirmed the importance of the texture information.

Discussion

What is the phenomenon that could explain the critical threshold showed on Figure 7 ? For the lowest porosities, pores induces thermal radiation scattering that lengthens the mean travel of the radiation and then increase the apparent optical thickness of the media. Also, the radiation path inside the ceramic was longer in comparison with those performed in the single crystal of same thickness. Hence, as the absorption is strengthened, the emissivity of the ceramic is greater than those of the single crystal. Furthermore, as the materials become more and more porous, scattering was more and more important and the emissivity increase, up to a critical porosity threshold. However, above this threshold, scattering was so important that backscattering becomes more efficient and induced progressively a decrease of the apparent optical thickness of the ceramic. Then, the radiation was less absorbed and the emissivity was lowered.

This behavior for porosities lower than the critical threshold was encountered for samples where the backscattered part of the radiation was weak in comparison with the transmitted part, or in other words, for samples having a diffuse transmissivity higher than the diffuse reflectivity [START_REF] Rozenbaum | [END_REF]. The opposite behavior was observed for porosity higher than the critical threshold, i.e. for samples having a diffuse reflectivity higher than the diffuse transmissivity.

The critical threshold represented the limit between a reflective (porosity>5%) and a transmissive behavior. All these explanations are in agreement with the results of a numerical simulation of radiation scattering in a porous media [START_REF] Rozenbaum | [END_REF]. For porosities higher than those presented in this paper, the optical thickness of the ceramics can probably be lower than the thickness of the single crystal and, as a result, the ceramics emissivity should be lower than the emissivity of the single crystal.

These explanations enable to understand the behavior observed on Figure 8 between the two ceramics with quasi the same total porosity but different textures. For wavenumbers higher than 1800 cm -1 , these two ceramics possessed an emissivity higher than the single crystal. In this range, due to the weak absorption coefficient, the radiation mean path inside the sample was higher than the thickness of the single crystal. Then, the emissivities of the ceramics are higher than those of the single crystal as previously observed. For wavenumbers between 1300 and 1800 cm -1 , the emissivity of the Al(D')-23.2 ceramic was lower than those of the single crystal. A qualitative comparison of the texture of both ceramics shows that the mean pore size of the Al(D')-23.2 ceramic is 40 times as high as the mean pore size of the Al(C)-20.6 ceramic (Figure 2 and Figure 3). This difference was sufficient to change drastically the nature of the radiation scattering in the Al(D')-23.2 ceramic. In this case, the mean size of the pore radius was about 10 µm, and the radiation scattering follows roughly the optical geometric laws. In this type of radiation scattering, backscattering was very efficient and drive for a one millimeter thick sample to a diffuse reflectivity much more important than the diffuse transmissivity. With these considerations it is concluded that the apparent optical thickness of the sample between 1300 and 1800 cm -1 is lower than those of the corresponding single crystal or in other words, only radiation of a small layer near the surface sample can contribute to the emissivity. In this case, backscattering was more efficient than the radiation absorption. On the contrary, for the CEA samples the mean size of the pore radius was about 0.25 µm, value that was sufficiently small to prevent scattering to follow optic geometric laws [START_REF] Rozenbaum | [END_REF]. Furthermore, the ceramic grains are small enough to allow frustrated reflection and then induced less efficient backscattering. For this sample and within this spectral range, absorption coefficient mastered the backscattering behavior and led to the observed result.

Then, the spectral radiative properties were completely dependent on the competition between the absorption coefficient (following the wavelength) and the radiative scattering.

Conclusion

In this paper, we showed the effect of extrinsic parameters such as porosity and texture on the thermal-radiative properties of alumina ceramics. Even if the behaviors observed for these materials are not valid for all ceramics, this rapid presentation pointed out the obligation to take into account these parameters. Besides, this paper emphasizes the different mistakes that could be made (and now avoided) in laboratory, industry or in design department without any care. As emissivity in the transparent zone depends on extrinsic parameters, it is not possible to predict the spectral value of emissivity only by the knowledge of intrinsic parameters (refractive index and extinction coefficient) and the thickness of a material. Indeed, as explained before, the modifications in the semitransparent and transparent zones were essentially due to the bulk texture and porosity. In the opaque zone, the increase and the spectral modification of the emissivity were mainly due to the structure of the ceramic surface. These results show for instance the necessity to have the exact characteristics of a ceramic to measure correctly its temperature with an optical pyrometer. In the same way, these textural changes must be taken into account in the input data used for modeling the heat transfer inside processes at high temperature such as a glass making furnace. In a future work, it will be interesting to verify if the critical porosity threshold observed for alumina ceramics is or not highly texture dependent.

Figures captions

Table 1: textural data for alumina ceramics. Figure 5 : influence of the porosity in the phonon zone on normal spectral emissivities of alumina ceramics (thickness=1 mm, T=1350 K). The normal spectral emissivity of an alumina single crystal (thickness=1 mm, T=1350 K) was given as reference.

Figure 6 : influence of the porosity in the transmission edge of alumina ceramics (thickness=1 mm, T=1350 K, from CEA). The normal spectral emissivity of an alumina single crystal (thickness=1 mm, T=1350 K) was given as reference.

Figure 7 : evolution of the normal spectral emissivity of alumina ceramics (thickness=1 mm) versus porosity: T=1350 K Figure 8 : normal spectral emissivity of alumina ceramics (thickness=1 mm, T=1350 K) with two different textures.

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Figure 1 :

 1 alumina ceramic Al(C)-3.8 (CEA). Sintering temperature: 1773 K. Porosity: 3.8%.

Figure 2 :

 2 alumina ceramic Al(C)-20.6 (CEA). Sintering temperature: 1623 K. Porosity: 20.6%.

Figure 3 :

 3 alumina ceramic Al(D')-23.2 (Desmarquest). Sintering temperature: 2003 K. Porosity: 23.2%.

Figure 4 :

 4 normal spectral emissivities of an alumina single crystal and alumina ceramics for various porosities. (thickness=1 mm, T=1350 K).

Table caption Table 1 :

 caption1 Main characteristics of the ceramics studied.