# Thermal and Structural Characterization of a Titanium Carbide/Carbon Composite for Nuclear Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{x}) target composed of seven thin 40 mm diameter disks that are axially spaced to optimize the dissipation by thermal radiation of the power deposited by a 40 MeV 200 μA proton beam, and it is used for the production of neutron-rich RIBs in the 80–160 amu mass range [8]. In the case of other specific nuclei of interest, e.g., neutron-deficient radionuclides, other refractory carbides such as silicon carbide (SiC), lanthanum carbide (LaC

_{x}), boron carbide (B4C), and titanium carbide (TiC) are being adopted as target materials, maintaining the same multi-disk-shaped architecture proposed for UC

_{x}. In particular, SiC was tested to produce aluminum RIBs at Oak Ridge National Laboratories (ORNL) in similar conditions [9] and is planned as the first material to be employed for the commissioning of the SPES facility, as it implies a lower radiological risk compared to UC

_{x}.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Production of the TiC samples

_{2}) as a precursor and graphite powder as a carbon source.

_{2}powder, no information was provided by the supplier about its crystalline form (rutile or anatase).

_{2}powder with the graphite in a ball mill at 400 rpm for 45 min. The powders were subsequently transferred into an agate mortar, where a phenol-formaldehyde resin in an acetone solution was added as a binder and manually incorporated into the powder mix, corresponding to 5% wt. of resin in the mix. After acetone evaporation, the obtained mixture was pressed in the form of 40 mm disk-shaped pellets under a uniaxial pressure of 300 MPa for 10 min.

^{−5}mbar) at 1900 °C with a heating rate of 2 °C/min, a dwell time of 24 h, and a cooling rate of 2 °C/min. Besides being necessary for the occurrence of Reaction (1), the thermal treatment also had the aim of favoring the partial sintering of the freshly formed TiC.

#### 2.3. Dimensional and Morphological Characterization

_{bulk}) of the resulting samples was then calculated as the ratio of the mass and the apparent volume after sintering. With such data, it was possible to calculate the total porosity (P) of the produced TiC disks using the following equation, considering a theoretical density (ρ

_{th}) of 3.38 g/cm

^{3}[23], which was calculated considering the volume fractions of TiC and C in the theoretical TiC + 2C composition:

#### 2.4. High-Temperature Thermal Characterization

^{−6}mbar, containing a graphite Ohmic heater. The latter was opportunely shaped to generate a circular hot spot of approximately 20 mm diameter at its center, whose temperature was uniform and could be increased up to 2000 °C by the stepwise increment of the heating current. A sample disk with a diameter between 30 and 40 mm was positioned and centered with the heater hot spot using three tungsten support rods, preventing direct contact with the graphite resistor. As a consequence, only radiative fluxes concurred with the sample heating since the contact with the support rods was punctual. The resulting sample temperature distribution typically exhibited a radial pattern with a hot spot at the center. In addition to the modulation of the heating current, the extent of the temperature gradient between the sample center and the periphery could be varied by adjusting the distance between the graphite resistor and the tested disk. The vacuum chamber was equipped with a borosilicate viewport positioned in correspondence with the top surface of the sample disk, allowing both visual observation and noncontact temperature measurements. In particular, the latter were performed using an infrared ratio pyrometer (IRCON

^{®}modline 5 R, Fluke Process Instrument, Everett, WA, USA) characterized by wavelength working bands of 0.75–1.05 μm and 1.0–1.1 μm in two-color mode and 1.0–1.1 μm in one-color mode and output temperature ranges of 600–1400 °C for the 5R-1410000 model and 1000–3000 °C for the 5R-3015000 model. When the instrument operated in one-color mode, accurate sample temperature measurements required spectral emissivity at ~1 μm ε

_{1 μm}of the surface of interest, which was often unknown, especially in the case of custom-manufactured samples. Conversely, when the pyrometer worked in two-color mode, the sample temperature was directly derived from the ratio of the infrared emission in the two working wavelength bands, without knowing the corresponding spectral emissivity value. The potential wavelength-dependent variation in the emission for each type of sample material was taken into account by opportunely setting the e-slope parameter, as recommended by the manufacturer.

_{1 μm}of the measured temperature.

^{®}, allowed the analysis of both the electrical problem and the radiative/conductive heat exchange processes (convection could be neglected thanks to the high-vacuum working conditions). In steady-state conditions, provided that the thermal and electrical characteristics of the graphite heater were well known, the model required the definitions of the temperature-dependent ε(T) and k(T) to accurately simulate the sample temperature field. The presented experimental routine allowed for the measurement of the normal spectral emissivity, ε

_{1 μm}(T), as a function of the acquired temperature. Concerning the thermal radiation problem, the model adopted the assumption of grey diffuse surfaces. Therefore, the required sample radiative property was the total hemispherical emissivity, ε

_{tot}(T). As highlighted in previous studies, the directional dependence of the radiation emission is generally negligible [25], and carbides are often reasonably assumed to be grey bodies, omitting the potential infrared wavelength influence. Consequently, the measured ε

_{1 μm}(T) could be considered a valid estimation of the ε

_{tot}(T) required for the ANSYS

^{®}model. With such hypotheses, it follows that k(T) provides the only unknown sample property. As proposed in previous works, the temperature-dependent thermal conductivity can be expressed within the FE model in the form of a second-degree polynomial, such as k(T) = C

_{0}+ C

_{1}T + C

_{2}T

^{2}. Therefore, the estimation of k(T) consisted of the numerical determination of the triplet of C

_{i}coefficients of the polynomial for which the computed temperature distribution was consistent with the experimentally measured data. In ANSYS

^{®}, this was handled as a typical optimization problem, where the C

_{i}coefficients were the optimization variables and the objective function was the residual function J(

**C**), expressed as Equation (3):

**C**is the Ci optimization variable vector, N corresponds to the number of heating current steps applied for the experimental measurements, ${\mathrm{T}}_{{\mathrm{C}}_{{\mathrm{FE}}_{\mathrm{i}}}}\text{}\left(C\right)$ and ${\mathrm{T}}_{{\mathrm{P}}_{{\mathrm{FE}}_{\mathrm{i}}}}\text{}\left(C\right)$ are the temperatures computed using the FE model at the center and periphery of the sample, respectively, and ${\mathrm{T}}_{{\mathrm{C}}_{{\mathrm{EXP}}_{\mathrm{i}}}}$ and ${\mathrm{T}}_{{\mathrm{P}}_{{\mathrm{EXP}}_{\mathrm{i}}}}$ are the corresponding experimental data. The optimization process was performed by using the ANSYS

^{®}APDL optimization tool to obtain the set of C

_{i}that minimize the residual function J(

**C**).

#### 2.5. Estimation of the Stress Limit through the Virtual Thermoelastic Parameter (VTP) Approach

_{lim}, is reached.

_{fract}, for which the sample failure was observed. At this point, the steady-state sample temperature distribution at the failure moment {T

_{fract}} was calculated using the same FE model adopted for the thermal conductibility estimation. In this case, the sample’s thermal properties, ε

_{tot}(T) and k(T), and the facture current intensity, I

_{fract}, were provided as input data. Subsequently, the FE model was used to perform a thermostructural analysis to compute the stress field that caused the sample failure {σ

_{fract}} once the proper thermoelastic properties were introduced. In steady-state conditions, for isotropic linear elastic materials, such as ceramics, the Young’s modulus, E; the Poisson’s ratio, ν; and the coefficient of thermal expansion, α, were the properties required to compute {σ} starting from {T}. The radial pattern of {T}, characterized by a sample center–periphery temperature gradient with a peak value at the center, produced a typical stress distribution with compression at the center of the disk, where both the radial and circumferential stress components, σ

_{r}and σ

_{θ}, respectively, were negative stresses (the axial component, σ

_{z}, was negligible since {σ} had an evident planar distribution). These stress components were not dangerous for the structural integrity of the disk. Conversely, at the sample periphery, the stress component σ

_{θ}exhibited its maximum positive value and corresponded to the maximum tensile first principal stress (σ

_{I}) within the sample. As ceramic materials are generally characterized by a weak resistance to tension, it was reasonable to ascribe the sample failure to the maximum positive value of the σ

_{θfract}component of the computed stress field {σ

_{fract}} at the disk periphery. This value could be identified as the critical tensile stress, σ

_{C}, of the considered specimen. The computed fracture stress data from the different samples were subsequently analyzed trough the Weibull statistical approach, which was applicable in the case of the brittle fracture of ceramic materials, as seen in the ASTM practice [26]. The material σ

_{lim}in the tested temperature range was determined as the stress associated with a survival probability of 99.99%.

_{lim}estimation is not trivial, as the thermoelastic material properties are often unknown and difficult to determine experimentally. For this reason, the virtual thermoelastic parameter (VTP) approach was theorized and presented in previous works, where it was applied the sake of comparison to fully characterized commercial silicon carbides. According to this approach, arbitrary temperature-independent values for the parameters E*, ν*, and α* can be assumed for the sake of the calculation of a virtual stress field {σ*}. In this way, it was possible to estimate a σ*

_{lim}of the material trough a Weibull analysis. With this reasonable assumption, if the same values of E*, ν*, and α* were used in the design phase of a target, it was possible to compare the computed maximum first principal stress, σ*

_{I MAX}, with the estimated σ*

_{lim}for the structural verification. Table 1 summarizes the adopted virtual thermoelastic parameters E*, ν*, and α*, which were extracted from available literature data at room temperature for other kinds of titanium carbides.

## 3. Results

#### 3.1. Production of the TiC Samples

#### 3.2. Dimensional and Morphological Characterization

_{2}were not performed since similar previous studies highlighted that a thermal treatment in vacuum at a temperature above 1700 °C ensures total oxide degradation [23,30,31]. All specimens exhibited crack-shaped pores that were homogenously distributed on the sample surface, confirming the expected high porosity.

#### 3.3. High-Temperature Thermal Characterization

#### 3.4. Estimation of the Stress Limit through the Virtual Thermoelastic Parameter (VTP) Approach

_{fract}, for which the sample failure occurs was identified when the fragments of the broken sample fell from the tungsten support rods and a sudden discontinuity in the pyrometer signal was reported. Consequently, a clear identification of I

_{fract}was not feasible in the case of the six incompletely cracked specimens since the pyrometer temperature measurement on the sample surface exhibited a continuous signal.

_{fract}and the last measured center temperature before breakage. It is relevant to highlight that such specimens were tested with different sample–heater distances, resulting in different temperature distributions at equal heating powers. Additionally, as highlighted in Table 4, failure occurred in most cases at a temperature lower than the maximum temperature level reached during the thermal characterization tests. Indeed, such experimental activity was performed on samples that did not exhibit evident signs of failure, similar to the specimen shown in Figure 6c.

_{fract}} was calculated with the VTP approach, and the maximum positive value of the σ*

_{θfract}component at the sample periphery was extracted, which corresponded to the critical tensile stress, σ*

_{C}, of the sample. These data were subsequently analyzed with the statistical Weibull approach according to the ASTM standard practice [26]. Figure 7 reports the resulting data distribution, with P

_{f}being the failure probability, which was calculated as follows:

_{lim}. This value was computed from the Weibull distribution, taking a failure probability of 0.01% as a reference, which corresponded to a survival probability of 99.99%.

## 4. Discussion

_{2}in the presence of a carbon source, was already consolidated in previous works [23,30]. However, in this study, this procedure was successfully used for the manufacture of approximately 40 mm diameter thin disks for the first time. This sample dimension was selected to guarantee the full compatibility of the manufactured specimens with the peculiar SPES ISOL target architecture [32]. The sample morphological and dimensional analysis confirmed the high repeatability of the production process since all samples exhibited very similar dimensions. Additionally, a high porosity above 50% was achieved, and SEM observations highlighted the presence of interconnected crack-shaped pores. On one hand, this microstructure is expected to promote the release of the produced nuclides when this material is used as an ISOL production target. For some specific radionuclides, such as scandium isotopes, previous studies highlighted that a high porosity may not be sufficient to promote an efficient nuclide release from titanium carbide [16,33]. The development of nanostructured target materials could overcome such limitations. On the other hand, the presence of cracks has a detrimental effect on the mechanical resistance of the material that can result in the material being highly prone to failure in the presence of the typical thermal stresses that arise during operation at a high temperature. This phenomenon is however mitigated by the presence of a consistent residual graphite phase that normally has a beneficial effect on the material’s mechanical resistance.

^{®}finite element model that accurately reproduced the experimental test bench. On average, the studied titanium carbide exhibited a thermal conductivity in the range of 8–10 W/m °C, with a slightly increasing trend as a function of the temperature. This rising behavior is ascribable to the presence of the dispersed graphite phase and was also observed for other composites with a graphite dispersion within a carbide matrix [24,34,35]. In addition, a similar range of thermal conductivity was also measured for a high-porosity silicon carbide in previous works [36].

^{−5}–10

^{−6}mbar [18]. Normally, this parameter is estimated by evaluating the weight loss of samples during a long-term heating process at a given uniform temperature. In the case of the considered material, several studies in the literature reported the range 1900 ÷ 2000 °C as the operational temperature for TiC with a disperse graphite phase [10,11,12,33]. Since the reported data referred to a material with a similar composition produced with the same approach, the experimental determination of the limit temperature was not necessary.

_{C}with VTP. Indeed, six samples did not exhibit any detectable evidence of failure. Therefore, their critical tensile stress values were not reached during the tests. Since all samples were tested with the same thermal treatment, it was reasonable to assume that the intact titanium carbide disks were characterized by higher critical tensile stress values than the specimens that shattered into two or more fragments. Additionally, two samples presented visible cracks but did not shatter into fragments, and neither crack propagated with subsequent heating cycles. Indeed, since the cracks stopped at the central region, the occurrence of compressive thermal stresses blocked the crack propagation during the test. For the application as a target at SPES, this failure scenario does not represent an issue. Indeed, if a target disk does not shatter into fragments, it can still operate for the production of RIBs. Furthermore, the presence of a crack significantly reduces the extent of the tensile stresses at the target’s periphery, decreasing its failure likelihood. For such reasons, the presented Weibull analysis, performed neglecting eight such samples, led to a more conservative estimation of the material’s σ*

_{lim}, as samples with higher σ*

_{C}values were not considered in the calculations. At this point, it is relevant to clarify that the computed σ*

_{lim}does not represent the absolute stress limit of the considered material, but it is a reference value that the target designer can adopt for design validations or operation condition evaluations as long as the thermal stress field is computed with the same virtual thermoplastic parameters that were adopted in this study.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Catherall, R.; Andreazza, W.; Breitenfeldt, M.; Dorsival, A.; Focker, G.J.; Gharsa, T.P.; Giles, T.J.; Grenard, J.-L.; Locci, F.; Martins, P.; et al. The ISOLDE facility. J. Phys. G Nucl. Part. Phys.
**2017**, 44, 094002. [Google Scholar] [CrossRef] [Green Version] - Bricault, P. Status report of the radioactive ion beam production at TRIUMF (invited). Rev. Sci. Instrum.
**2006**, 77, 03A710. [Google Scholar] [CrossRef] - Radford, D.C.; Baktash, C.; Galindo-Uribarri, A.; Gross, C.J.; Lewis, T.A.; Mueller, P.E.; Hausladen, P.A.; Shapira, D.; Stracener, D.W.; Yu, C.-H.; et al. Physics with heavy neutron-rich RIBs at the HRIBF. In Exotic Nuclei and Atomic Masses; Springer: Berlin/Heidelberg, Germany, 2003; pp. 291–293. [Google Scholar] [CrossRef] [Green Version]
- Santos, F.D.O.; Himpe, P.; Lewitowicz, M.; Stefan, I.; Smirnova, N.; Achouri, N.L.; Angelique, J.C.; Angulo, C.; Axelsson, L.; Baiborodin, D.; et al. Study of 19Na at SPIRAL. Eur. Phys. J. A
**2005**, 24, 237–247. [Google Scholar] [CrossRef] [Green Version] - Azaiez, F.; Essabaa, S.; Ibrahim, F.; Verney, D. The ALTO Facility in Orsay. Nucl. Phys. News
**2013**, 23, 5–10. [Google Scholar] [CrossRef] - Andrighetto, A.; Manzolaro, M.; Corradetti, S.; Scarpa, D.; Monetti, A.; Rossignoli, M.; Ballan, M.; Borgna, F.; D’Agostini, F.; Gramegna, F.; et al. Spes: An intense source of Neutron-Rich Radioactive Beams at Legnaro. J. Phys. Conf. Ser.
**2018**, 966, 012028. [Google Scholar] [CrossRef] - Ramos, J.; Ballan, M.; Egoriti, L.; Houngbo, D.; Rothe, S.; Augusto, R.D.S.; Gottberg, A.; Dierckx, M.; Popescu, L.; Marzari, S.; et al. Design and tests for the new CERN-ISOLDE spallation source: An integrated tungsten converter surrounded by an annular UC target operated at 2000 °C. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2019**, 463, 357–363. [Google Scholar] [CrossRef] - Corradetti, S.; Andrighetto, A.; Manzolaro, M.; Scarpa, D.; Vasquez, J.; Rossignoli, M.; Monetti, A.; Calderolla, M.; Prete, G. Research and development on materials for the SPES target. EPJ Web Conf.
**2014**, 66, 11009. [Google Scholar] [CrossRef] [Green Version] - Barbui, M.; Andrighetto, A.; Antonucci, C.; Biasetto, L.; Carturan, S.; Cervellera, F.; Cevolani, S.; Cinausero, M.; Colombo, P.; Dainelli, A.; et al. Calculations and first results obtained with a SiC prototype of the SPES direct target. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2008**, 266, 4289–4293. [Google Scholar] [CrossRef] - Carraz, L.; Haldorsen, I.; Ravn, H.; Skarestad, M.; Westgaard, L. Fast release of nuclear reaction products from refractory matrices. Nucl. Instrum. Methods
**1978**, 148, 217–230. [Google Scholar] [CrossRef] - Hoff, P.; Jonsson, O.; Kugler, E.; Ravn, H. Release of nuclear reaction products from refractory compounds. Nucl. Instrum. Methods Phys. Res.
**1984**, 221, 313–329. [Google Scholar] [CrossRef] [Green Version] - Hanemaayer, V.; Bricault, P.; Dombsky, M. Composite ceramic targets for high power proton irradiation. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2008**, 266, 4334–4337. [Google Scholar] [CrossRef] - Ashford, M.; Popescu, L.; Houngbo, D.; Dierckx, M.; Abderrahim, H.A. Exploratory study for the production of Sc beams at the ISOL facility of MYRRHA preliminary thermal investigations. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2019**, 463, 244–247. [Google Scholar] [CrossRef] - Galevsky, G.V.; Rudneva, V.V.; Garbuzova, A.K.; Valuev, D.V. Titanium Carbide: Nanotechnology, Properties, Application. IOP Conf. Ser. Mater. Sci. Eng.
**2015**, 91, 012017. [Google Scholar] [CrossRef] [Green Version] - Tusseau-Nenez, S.; Roussière, B.; Barré-Boscher, N.; Gottberg, A.; Corradetti, S.; Andrighetto, A.; Mhamed, M.C.; Essabaa, S.; Franberg-Delahaye, H.; Grinyer, J.; et al. Characterization of uranium carbide target materials to produce neutron-rich radioactive beams. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2016**, 370, 19–31. [Google Scholar] [CrossRef] - Ramos, J.; Gottberg, A.; Augusto, R.; Mendonca, T.; Riisager, K.; Seiffert, C.; Bowen, P.; Senos, A.; Stora, T. Target nanomaterials at CERN-ISOLDE: Synthesis and release data. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2016**, 376, 81–85. [Google Scholar] [CrossRef] [Green Version] - Gottberg, A. Target materials for exotic ISOL beams. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2016**, 376, 8–15. [Google Scholar] [CrossRef] - Manzolaro, M.; Corradetti, S.; Ballan, M.; Salomoni, R.; Andrighetto, A.; Meneghetti, G. Thermal and Mechanical Characterization of Carbides for High Temperature Nuclear Applications. Materials
**2021**, 14, 2689. [Google Scholar] [CrossRef] [PubMed] - Rahman, M.T.; Hoque, A.; Azmi, M.M.; Gafur, M.A.; Khan, R.A.; Hossain, M.K. Fe2O3 nanoparticles dispersed unsaturated polyester resin based nanocomposites: Effect of gamma radiation on mechanical properties. Radiat. Eff. Defects Solids
**2019**, 174, 480–493. [Google Scholar] [CrossRef] - Rahman, M.; Hoque, A.; Gafur, M.; Khan, R.A.; Hossain, M.K. Study on the mechanical, electrical and optical properties of metal-oxide nanoparticles dispersed unsaturated polyester resin nanocomposites. Results Phys.
**2019**, 13, 102264. [Google Scholar] [CrossRef] - Khan, S.; Hossain, M.K. Classification and properties of nanoparticles. In Nanoparticle-Based Polymer Composites; Woodhead Publishing: Sawston, UK, 2022; pp. 15–54. [Google Scholar] [CrossRef]
- Corradetti, S.; Carturan, S.; Andrighetto, A.; Mariotto, G.; Giarola, M.; Fabrizi, A.; Maddalena, A.; Biasetto, L. Graphene derived lanthanum carbide targets for the SPES ISOL facility. Ceram. Int.
**2017**, 43, 10824–10831. [Google Scholar] [CrossRef] - Corradetti, S.; Carturan, S.; Maggioni, G.; Franchin, G.; Colombo, P.; Andrighetto, A. Nanocrystalline titanium carbide/carbon composites as irradiation targets for isotopes production. Ceram. Int.
**2019**, 46, 9596–9605. [Google Scholar] [CrossRef] - Manzolaro, M.; Corradetti, S.; Andrighetto, A.; Ferrari, L. A steady-state high-temperature method for measuring thermal conductivity of refractory materials. Rev. Sci. Instrum.
**2013**, 84, 054902. [Google Scholar] [CrossRef] [PubMed] - Bergman, T.L.; Bergman, T.L.; Incropera, F.P.; DeWitt, D.P.; Lavine, A.S. Fundamentals of Heat and Mass Transfer; Wiley: Hoboken, NJ, USA, 2011; ISBN 047131272X. [Google Scholar]
- ASTM C1239-07; Standard Practice for Reporting Uniaxial Strength Data and Estimating Weibull Distribution Parameters for Advanced Ceramics. ASTM International: West Conshohocken, PA, USA. Available online: https://www.astm.org (accessed on 30 August 2022).
- Ma, Y.; Bao, C.; Song, S.; Lei, J. Effects of TiC addition on microstructures, mechanical properties and fracture behaviors of porous titanium carbide ceramics. Ceram. Int.
**2018**, 44, 19919–19925. [Google Scholar] [CrossRef] - Storms, E.K.; Margrave, J.L. The Refractory; Elsevier Science: Amsterdam, The Netherlands, 2016; ISBN 9781483271774. [Google Scholar]
- Pierson, H.O. Handbook of Refractory Carbides & Nitrides: Properties, Characteristics, Processing and Application; Elsevier Science: Amsterdam, The Netherlands, 1996; ISBN 9780815517702. [Google Scholar]
- Zanini, A.; Corradetti, S.; Carturan, S.M.; Colombo, P.; Andrighetto, A.; Franchin, G. Sucrose-based sol-gel synthesis of microporous titanium carbide as target material for the production of radioisotopes. Microporous Mesoporous Mater.
**2022**, 337, 111917. [Google Scholar] [CrossRef] - Corradetti, S.; Carturan, S.; Biasetto, L.; Andrighetto, A.; Colombo, P. Boron carbide as a target for the SPES project. J. Nucl. Mater.
**2013**, 432, 212–221. [Google Scholar] [CrossRef] - Monetti, A.; Andrighetto, A.; Petrovich, C.; Manzolaro, M.; Corradetti, S.; Scarpa, D.; Rossetto, F.; Dominguez, F.M.; Vasquez, J.; Rossignoli, M.; et al. The RIB production target for the SPES project. Eur. Phys. J. A
**2015**, 51, 128. [Google Scholar] [CrossRef] - Ramos, J.; Stora, T.; Senos, A.; Bowen, P. Thermal stability of nanometric TiC-carbon composites: Effects of carbon allotropes and Zr milling impurities. J. Eur. Ceram. Soc.
**2018**, 38, 4882–4891. [Google Scholar] [CrossRef] - Corradetti, S.; Manzolaro, M.; Andrighetto, A.; Zanonato, P.; Tusseau-Nenez, S. Thermal conductivity and emissivity measurements of uranium carbides. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. Atoms
**2015**, 360, 46–53. [Google Scholar] [CrossRef] - Corradetti, S.; Carturan, S.M.; Ballan, M.; Eloirdi, R.; Celdran, P.A.; Walter, O.; Staicu, D.; Blanco, O.D.; Andrighetto, A.; Biasetto, L. Effect of graphite and graphene oxide on thorium carbide microstructural and thermal properties. Sci. Rep.
**2021**, 11, 9058. [Google Scholar] [CrossRef] - Silvestroni, L.; Corradetti, S.; Manzolaro, M.; Ballan, M.; Cesarotto, D.; Sciti, D.; Zoli, L. Novel SiC/C composite targets for the production of radioisotopes for nuclear applications. J. Eur. Ceram. Soc.
**2022**, 42, 6750–6756. [Google Scholar] [CrossRef]

**Figure 1.**The experimental test bench adopted for the measurement of the sample emissivity and temperature data necessary for the thermal conductivity estimation: general CAD view (

**a**), detailed view of the sample and heater (

**b**), and pictures of the components at high temperature during a test with a TiC specimen (

**c**).

**Figure 4.**Estimated thermal conductivity for three different samples with the corresponding 95% confidence bounds (CBs).

**Figure 5.**Comparison between the experimental and numerically calculated temperature values at the center and periphery of sample 1.

**Figure 6.**The three outcomes of the performed thermal stress failure tests: complete failure (

**a**), incomplete crack propagation (

**b**), and no evident cracking (

**c**).

**Table 1.**Elastic properties from the literature, which were adopted for the calculation of the stress field according to the virtual thermoelastic parameter approach.

Young’s Modulus (E*) | Poisson’s Ratio (ν*) | Coefficient of Thermal Expansion (α*) |
---|---|---|

3220 (MPa) [27] | 0.191 [28] | 7.4∙10^{−6} (1/°C) [29] |

**Table 2.**Summary of the average dimensions of the produced TiC samples before and after the thermal treatment.

Before Thermal Treatment | After Thermal Treatment | |
---|---|---|

Diameter (mm) | 40.5 ± 0.2 | 36.6 ± 0.7 |

Thickness (mm) | 1.56 ± 0.05 | 1.57 ± 0.06 |

**Table 3.**The average mass of the produced TiC samples before and after the thermal treatment and the achieved average porosity.

Average Mass before Thermal Treatment (g) | Average Mass after Thermal Treatment (g) | Average Mass Loss | Average Porosity |
---|---|---|---|

3.97 ± 0.07 | 2.34 ± 0.12 | 41 ± 3% | 58 ± 3% |

Sample Number | Sample Thickness (mm) | Sample Diameter (mm) | Heater-Sample Distance (mm) | Fracture Current Intensity (I_{fract}) (A) | Center Temperature at the Fracture (°C) |
---|---|---|---|---|---|

1 | 1.53 | 35.95 | 3.11 | 165 | 752 |

2 | 1.51 | 36.06 | 3.11 | 150 | 892 |

3 | 1.58 | 35.95 | 3.11 | 160 | 999 |

4 | 1.61 | 36.34 | 4.77 | 160 | 966 |

5 | 1.61 | 36.08 | 3.11 | 170 | 1032 |

6 | 1.63 | 36.24 | 3.11 | 170 | 1040 |

7 | 1.62 | 35.87 | 3.11 | 190 | 1131 |

8 | 1.57 | 36.00 | 1.22 | 160 | 1369 |

9 | 1.55 | 36.07 | 1.22 | 120 | 814 |

10 | 1.63 | 36.17 | 1.85 | 140 | 917 |

11 | 1.62 | 36.24 | 1.85 | 140 | 874 |

12 | 1.58 | 36.07 | 3.11 | 140 | 874 |

13 | 1.62 | 36.02 | 3.11 | 160 | 960 |

14 | 1.55 | 35.81 | 1.22 | 150 | 951 |

15 | 1.62 | 36.17 | 1.22 | 120 | 795 |

16 | 1.65 | 36.12 | 1.85 | 140 | 851 |

**Table 5.**The Weibull distribution parameters (with 90% confidence bounds) and the referential stress limit calculated with the VTP approach.

$\widehat{\mathbf{m}}$ (/) (Lower Bound) | $\widehat{\mathbf{m}}$ (/) (Average) | $\widehat{\mathbf{m}}$ (/) (Upper Bound) | $\widehat{\mathsf{\sigma}}$_{θ} (MPa)(Lower Bound) | $\widehat{\mathsf{\sigma}}$_{θ} (MPa)(Average) | $\widehat{\mathsf{\sigma}}$_{θ} (MPa)(Upper Bound) | σ*_{LIMIT} (MPa) | Temperature Range (°C) |
---|---|---|---|---|---|---|---|

3.72 | 5.72 | 7.38 | 2.03 | 2.21 | 2.40 | 0.44 | 700 ÷ 1400 |

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**MDPI and ACS Style**

Ballan, M.; Corradetti, S.; Manzolaro, M.; Meneghetti, G.; Andrighetto, A.
Thermal and Structural Characterization of a Titanium Carbide/Carbon Composite for Nuclear Applications. *Materials* **2022**, *15*, 8358.
https://doi.org/10.3390/ma15238358

**AMA Style**

Ballan M, Corradetti S, Manzolaro M, Meneghetti G, Andrighetto A.
Thermal and Structural Characterization of a Titanium Carbide/Carbon Composite for Nuclear Applications. *Materials*. 2022; 15(23):8358.
https://doi.org/10.3390/ma15238358

**Chicago/Turabian Style**

Ballan, Michele, Stefano Corradetti, Mattia Manzolaro, Giovanni Meneghetti, and Alberto Andrighetto.
2022. "Thermal and Structural Characterization of a Titanium Carbide/Carbon Composite for Nuclear Applications" *Materials* 15, no. 23: 8358.
https://doi.org/10.3390/ma15238358