Thermal and mechanical properties of polycrystalline U₃Si₂ synthesized by spark plasma sintering

ABSTRACT

U₃Si₂ has been explored as an alternative nuclear fuel material for increased accident tolerance. However, scatter has been reported in the thermal properties possibly because of the pores and impurities within the samples. In the present study, we prepared a polycrystalline U₃Si₂ bulk sample with high density and without impurity, and evaluated its thermal and mechanical properties. The sample was synthesized by arc melting and spark plasma sintering, followed by annealing. The density of the U₃Si₂ pellet was 96% of the theoretical density. The heat capacity was measured and compared with the calculation data. In addition, the measured data were used to evaluate thermal conductivity of U₃Si₂. The measurement data of elastic properties were compared with the theoretical calculation and agreed well. A high thermal conductivity and hardness compare to UO₂make it favorable to anticipated as alternative nuclear fuel.

KEYWORDS:

• Uranium
• fuel
• light water reactor
• density
• thermal conductivity
• temperature dependence
• mechanical property

1. Introduction

The Fukushima accident in Japan highlighted the need for the development of accident tolerant fuel (ATF) and has become a primary focus for nuclear research. Several candidates such as U₃Si₂, U₃Si, and UN have been explored as new nuclear fuels within the framework of ATFs. These materials have attracted attention primarily because they have higher uranium density and thermal conductivity than UO₂, the current nuclear fuel for light water reactors. A higher density of uranium increases the fissile density, which compensates for the neutronic inefficiency of advanced cladding materials without increasing enrichment limits [1]. Higher thermal conductivity will improve the heat removal efficiency, reducing thermal stress when the reactor loses the coolant [2,3]. To utilize these candidates as alternative nuclear fuels, an accurate understanding of their thermal and mechanical properties is important to fabricate on a commercial manufacturing scale. Thus, the basic physical properties of these materials have been actively studied over the last several years [4–6].

The thermal conductivities of U₃Si₂, U₃Si, and UN are 8.5, 13.5, and 13.0 W/mK at 300 K, respectively, and increase with temperature. Since the thermal conductivity of UO₂ (9.8 W/mK at 300 K) decreases with temperature, U₃Si₂, U₃Si, and UN show significantly higher thermal conductivity than UO₂ at elevated temperature [7,8]. In addition, U₃Si₂, U₃Si, and UN possess high uranium densities of 11.3, 14.7, and 14.3 g-U/cm³, respectively, which are higher than that of UO₂ (9.7 g-U/cm³) [7]. However, U₃Si swells considerably under irradiation, and a phase transition occurs above 1000 K [9,10]. Furthermore, it was reported to be technically difficult to fabricate a high density UN pellet due to its high melting point (3078 K) [11]. In addition, U₃Si₂ is susceptible to chemical reaction. From this perspective, U₃Si₂ is likely the most promising candidate due to its favorable properties.

U₃Si₂ has a tetragonal structure (P4/mbm space group), a melting point of 1887 K, and useful properties as a nuclear fuel such as thermally stability at high temperatures as well as high corrosion and oxidation resistance [12]. For this reason, several groups have investigated the thermal properties of U₃Si₂ [7,13–17]. However, there is a distinct scatter in the reported values. For example, the thermal conductivity has been reported as 8.5–25.1 W/mK from 300 to 1770 K for sintered samples [7], 9.7–21.3 W/mK from 300 to 1400 K for arc casted samples [17], and 8.2–12.3 W/mK from 300 to 1121 K for induction casted samples [17]. The heat capacity value used to obtain the thermal conductivity also varies depending on the research group: from 160 to 180 J/molK over the temperature range 300–700 K [15] and from 140 to 166 J/molK over the temperature range 300–1300 K [7,16]. Furthermore, the linear thermal expansion coefficient (LTEC) reported by White et al. [7] abruptly decreased at 1100 K while others reported an almost constant value over the same temperature range [13,14]. The discrepancies observed for the thermal properties may be due to impurities, as observed in White’s (USi and UO₂) [7] and Taylor’s (USi₃) [15] studies, or voids in the measured samples, such as the low density of the specimen reported by Shimizu (92% T.D) [17]. Recently, Metzger et al. reported the Vickers hardness and fracture toughness of U₃Si₂ [18]. However, the sample they used for measurement contained USi and U₃Si₅ impurity phases, which could have greatly influenced the measured values.

Thus, in the present study, we report the thermal and mechanical properties of U₃Si₂. To obtain reliable data, we synthesized a dense polycrystalline U₃Si₂ sample without impurity. We evaluated thermal properties such as the thermal expansion coefficient, thermal conductivity, and heat capacity as well as mechanical properties such as the Debye temperature, elastic moduli, and hardness. We also calculated the heat capacity based on the lattice vibrations, thermal expansions, and electrical contribution and compared this estimate with the experimental values. Lastly, the experimental values obtained in the present study were compared with the available literature values regarding the properties of U₃Si₂.

2. Experimental procedure

The nominal composition of U₃Si₂ was prepared from natural uranium (Nuclear Fuel Industries, Ltd.) and silicon, 11N (KT’s craft Co., Ltd.) by arc melting in an Ar atmosphere. A 2 wt % excess Si was added to compensate for the evaporation of Si during arc melting. The ingot obtained was sealed into a SiO₂ tube and annealed at 1073 K for 24 h under vacuum. The produced ingot was then crushed into fine powder by ball milling at 200 rpm for 2 h with tungsten carbide vials and balls. The sample was prepared in a glove box under an Ar atmosphere to prevent oxidation. The obtained powder was sintered using spark plasma sintering (SPS) used carbon dye (size: 10 mm) at 1123 K under a pressure of 75 MPa for 10 min (Dr. Sinter SPS-515A, Sumitomo Coal Mining Co., Ltd.). Ar flow was maintained during the sintering process.

The crystal structures of the powder samples were analyzed by X-ray diffraction (XRD) using Cu-Kα radiation with a Rigaku Ultima IV X-ray diffractometer equipped with a scintillation counter. The lattice parameter dependence on temperature was measured by high temperature XRD (HT-XRD). Measurements were conducted in a He flow atmosphere from 300 to 1073 K. The lattice parameters were evaluated from the XRD peak positions using a least square method with NIST Si for angular calibration. The theoretical density was calculated from the lattice parameters, and the relative density was calculated by comparing the theoretical and measured densities obtained from the measured weight and dimensions of the sample. The thermal expansion coefficient was quantified based on the a and c axes of the lattice parameters measured by HT-XRD. The sample microstructures were observed using field emission scanning electron microscopy (FE-SEM, JEOL, JSM-6500F), and chemical compositions were determined by energy dispersive X-ray (EDX) spectroscopy of which results are shown in Table 1. The thermal expansion coefficient was also evaluated using a dilatometer (Bruker AXS, TD5000SA) from 300 to 1200 K. An Al₂O₃ reference sample was used for calibration. Heat capacity was measured using a differential scanning calorimeter (DSC, Jupiter, Netzsch) apparatus from 300 to 1200 K under Ar flow. This measurement was calibrated using a sapphire standard sample.

Table 1. Composition of the U₃Si₂ bulk sample after annealing, as analyzed by SEM/EDX

Element	Nominal composition (Mole fraction)	After annealing (Mole fraction)
U	0.593	0.61
Si	0.407	0.39

The thermal conductivity (λ) was calculated from the thermal diffusivity (D), specific heat capacity (C_p), and density (ρ). Thermal diffusivity was measured by the laser flash (LF) method using a LFA-457 (Netzsch) apparatus. Thermal diffusivity measurements were repeated three times at each temperature, and the standard error of measurement was found to be less than 3%. In addition, the temperature-dependent thermal diffusivity of the graphite standard sample was measured from 300 to 1073 K and compared to the literature value (NMIJ RM 1201-a) [19]. The deviations between the literature and measured values were also less than 3%. The longitudinal and shear sound velocities were measured using the ultrasonic pulse-echo method using a sing around ultrasonic instrument (ULTRASONIC ENGINEERING CO., LTD. UVM-2) to evaluate the elastic properties and Debye temperature. The longitudinal sound velocity of an iron standard sample was measured and compared with literature values [20]. The deviation between these values was less than 0.4%. Measurements were performed three times, and the standard error of the velocity was calculated and listed as uncertainties in Table 2. The Vickers indentation test was performed using a Vickers hardness tester (Akashi, hardness tester). The applied load was 9.8 N with a loading time of 10 s, and a series of 11 indentations were placed on the surface. The standard error for the Vickers hardness and fracture toughness are shown in Table 3 as uncertainties.

Table 2. Sample characteristics and thermophysical properties of U₃Si₂, UO₂, and UN [5,26,30,33,35,36,38,39,48,49]

Crystal system		Tetragonal		Cubic	Cubic
		U3Si2 [Experimental]	U3Si2 [Calculation] ^33	UO2	UN
Lattice parameter (Å)	a axis	7.321 ± 0.014	–	5.47 ^[Citation26]	4.89 ^[Citation49]
	c axis	3.894 ± 0.011	–	–	–
Sample bulk density (g/cm^3)	ρ	11.79 (96% T.D)	–	10.9 ^[Citation5]	14.3 ^[Citation5]
Melting point (K)	Tm	1935 ^[Citation30]	–	3138 ^[Citation5]	3123 ^[Citation5]
Average linear thermal expansion (K^−1)	αP
Dilatometer		16.4 ± 0.2 × 10^−6 (300–873 K)	–	9.76 × 10^−6 [Citation48]	7.096 × 10^−6 [Citation48]
HT-XRD		15.8 ± 1.3 × 10^−6 (300–1073 K)	–	–	–
Longitudinal velocity (ms^−1)	VL	3772 ± 26	3865	5400 ^[Citation35]	4750 ^[Citation36]
Shear sound velocity (ms^−1)	VS	2310 ± 2	2355	2800 ^[Citation35]	2640 ^[Citation36]
Shear modulus (GPa)	G	62.9 ± 0.1	67	83 ^[Citation35]	98 ^[Citation36]
Young’s modulus (GPa)	E	151.0 ± 0.9	163	221 ^[Citation35]	254 ^[Citation36]
Bulk modulus (GPa)	B	83.9 ± 2.3	92	209 ^[Citation35]	184 ^[Citation36]
Poisson’s ratio	v	0.20 ± 0.1	0.20	0.32 ^[Citation35]	0.27 ^[Citation36]
Debye temperature (K)	θD	275.5 ± 0.3	280	379 ^[Citation35]	364 ^[Citation36]
Grüneisen parameter	γ	2.39 ± 0.03	-	2.2 ^[Citation39]	2.0 ^[Citation38]

Table 3. Vickers hardness and fracture toughness of U₃Si₂ at 9.8 N together with the diagonal average (a) and c/a ratio

Sample	a [µm]	c/a	Vickers hardness HV [GPa]	Fracture toughness KIC [MPa·m^1/2]
U3Si2	24.55 ± 0.76	2.93	7.51 ± 0.41	3.25 ± 0.20

3. Results and discussion

The XRD patterns of the powder U₃Si₂ after arc melting, SPS, and annealing, along with the literature data are shown in Figure 1. All peaks were indexed on a tetragonal C11b-structured U₃Si₂ [21]. The lattice parameters of U₃Si₂ were evaluated from XRD patterns of the annealed sample and found to be 0.7321 ± 0.0014 nm for the a-axis and 0.3894 ± 0.0011 nm for the c-axis, which agreed with previously reported data [22]. The relative density of the prepared sample exceeded 96% of the theoretical density. To confirm the U and Si elemental distributions and the composition of the annealed sample, quantitative EDX analysis was performed, and the results are shown in Figure 2 and Table 1. The analysis confirmed that U and Si were distributed uniformly. The determined mole fractions were 0.61 for U and 0.39 for Si, which are quite close to the theoretical value of U₃Si₂. Based on these results, we concluded that a dense sample with a single phase of tetragonal C11b-structure U₃Si₂ was obtained.

Figure 1. XRD patterns of the U₃Si₂ powder together with the literature data for tetragonal structured U₃Si₂ [PDXL. (No: 01–075-1941).].

Figure 2. Microstructure of U₃Si₂ from field emission scanning electron microscopy (FE-SEM) and energy dispersive X-ray analysis.

The temperature-dependent lattice parameters are shown in Figure 3. The lattice parameters of both axes increase linearly with increasing temperature. The lattice parameters for the a and c axes were fit using the following linear expressions:

Figure 3. Lattice parameters a and c of U₃Si₂ as a function of temperature. The solid line is the fitting line expressed in Eqs. (1)(1) $a\left(T\right)=\left(0.7323\pm 0.006\right)\hspace{0.17em}+\hspace{0.17em}\left(7.3881\pm 1.2460\times {10}^{-6}T\right)\mathrm{n}\mathrm{m}$(1) and (2)(2) $c\left(T\right)=\left(0.3909\pm 0.0004\right)\hspace{0.17em}+\hspace{0.17em}\left(1.7415\pm 0.4847\times {10}^{-6}T\right)\mathrm{n}\mathrm{m}$(2) .

(1) $a\left(T\right)=\left(0.7323\pm 0.006\right)\hspace{0.17em}+\hspace{0.17em}\left(7.3881\pm 1.2460\times {10}^{-6}T\right)\mathrm{n}\mathrm{m}$(1)

(2) $c\left(T\right)=\left(0.3909\pm 0.0004\right)\hspace{0.17em}+\hspace{0.17em}\left(1.7415\pm 0.4847\times {10}^{-6}T\right)\mathrm{n}\mathrm{m}$(2)

where T is temperature in Kelvin. The fitted results are shown in Figure 3 as solid lines.

The volumetric thermal expansion coefficient (β) can be defined from the temperature-dependent lattice volume V. The corresponding relationship is as follows [23]:

(3) $\beta =\frac{1}{V_0^{\hspace{0.17em}}}\frac{\left(V-V_0\right)}{\left(T-T_0\right)}$(3)

where V₀ is the lattice volume at 300 K. The volumetric thermal expansion coefficient is β = 3α_l where α_l is the LTEC. Using this relationship, the average LTEC measured by HT-XRD was found to be 15.8 ± 1.3 × 10⁻⁶ K⁻¹ from 300 to 1073 K. In addition, we measured the thermal expansion of U₃Si₂ using a dilatometer. The thermal expansion (L-L₀)/L₀ is shown in Figure 4(a) where L is the measured sample length and L₀ is the length of the sample at 300 K. The LTEC can be defined as follows:

Figure 4. (a) Specimen length change and linear thermal expansion coefficient (LTEC) of U₃Si₂ as a function of temperature. (b) LTEC as a function of temperature together with previously reported data.

${\alpha }_{\mathrm{l}}=\frac{1}{L_0}\frac{\left(L-L_0\right)}{\left(T-T_0\right)}$ (4) The values of α_l calculated using Eq. (4) are plotted in Figure 4(a). The LTEC measured by dilatometer is almost constant from 300 to 873 K; however, over 873 K, the value slightly increased. The average LTEC was found to be 16.4 ± 0.2 × 10⁻⁶ K⁻¹ (dilatometer) from 300 to 873 K, and 15.8 ± 1.3 × 10⁻⁶ K⁻¹ (HT-XRD) from 300 to 1073 K, as listed in Table 2.

The LTECs obtained from the HT-XRD and dilatometer were plotted together with literature values in Figure 4(b). For the HT-XRD and dilatometer data, although the temperature dependencies of the LTECs are slightly different, the mismatch is quite small. The thermal expansion coefficient measured in the present study (HT-XRD and dilatometer) and shown in Figure 4(b) agreed with literature values reported by other groups [7,13,14].

Given that the thermal expansion coefficient is constant, the density of U₃Si₂ as a function of temperature can be calculated from the following:

(5) $\rho =\frac{{\rho }_0}{\left(1+\beta (T-T_0)\right)}=\frac{{\rho }_0}{\left(1+3{\alpha }_{\mathrm{l}}(T-T_0)\right)}$(5)

where T₀ is 300 K and ρ₀ is the density at T₀ (11.79 g/cm³), α_l is the LTEC obtained by HT-XRD and dilatometry. The calculated density as a function of temperature is shown in Figure 5. The temperature-dependent density calculated from LTEC obtained by HT-XRD (ρ_HT-XRD) is expressed as a linear function, and that obtained by dilatometer (ρ_dilatometer) was shown by data points which are fitted by a linear function. The functional forms are given by:

Figure 5. Density as a function of temperature. The black open solid symbols are the values obtained from dilatometry and the red line is from the high temperature X-ray diffraction analysis.

(6) ${\rho }_{\mathrm{H}\mathrm{T}-\mathrm{X}\mathrm{R}\mathrm{D}}=\left(11.96\pm 0.04\right)-\left(5.47\pm 0.01\times {10}^{-4}T\right),$(6)

(7) ${\rho }_{\mathrm{d}\mathrm{i}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{e}\mathrm{r}}=\left(11.88\pm 0.02\right)-\left(2.70\pm 0.50\times {10}^{-4}T\right)$(7)

Based on Lindemann melting rule, LTEC is inversely proportional to the melting temperature, T_m [24], i.e.:

(8) ${\alpha }_l{T}_m=C$(8)

where C is a constant. It has been reported that C is 0.03 for fluorite type oxides [25] and 0.077 for uranium intermetallic compounds [26]. For uranium metal, C was found to be 0.05 in the present study using the literature data [27]. The relationship between the melting temperature, T_m, and average LTEC, α_l, for U₃Si₂ [7,13,17] together with the other uranium containing compounds [26–29] is shown in Figure 6. The melting point for U₃Si₂ was taken from the literature [30] and is listed in Table 2. Figure 6 shows that the value of C for U₃Si₂ is quite close to 0.03, which is the same as fluorite type oxides, such as UO₂. This result may suggest that atomic bonding in U₃Si₂ is more similar to that in UO₂, compared to those in other uranium intermetallic compounds.

Figure 6. Relationship between the LTEC and melting point for U₃Si₂ and related compounds.

The elastic constants for Young’s modulus (E), shear modulus (G), bulk modulus (B), Poisson’s ratio (v), and Debye temperature ($\theta$_D) can be estimated from the longitudinal sound velocity (V_L) and shear sound velocity (V_S) as follows [31,32]:

(9) $G=\rho V_S^2$(9)

(10) $E=\frac{G(3V_L^2-4V_S^2)}{(V_L^2-V_S^2)}$(10)

(11) $B=\rho (V_L^2-\frac{4}{3}{V}_S^2)$(11)

(12) $v=\frac{1}{2}\frac{V_L^2-2V_S^2}{V_L^2-V_S^2}$(12)

(13) ${\theta }_{\mathrm{D}}=\left(\frac{\mathrm{h}}{{\mathrm{k}}_{\mathrm{B}}}\right)\cdot {\left[\frac{3n}{4\pi }\left(\frac{{\mathrm{N}}_{\mathrm{A}}\rho }{M}\right)\right]}^{1/3}{V}_m$(13)

(14) $V_m={\left[\frac{1}{3}\left(\frac{2}{V_S^3}+\frac{1}{V_L^3}\right)\right]}^{-1/3}$(14)

where h is Plank’s constant, k_B is Boltzmann’s constant, N_A is Avogadro’s constant, M is the molecular weight, and n is the number of atoms in the molecule. We used our experimentally measured data for longitudinal sound velocity V_L and shear sound velocity V_S which were 3772 ± 26 and 2310 ± 2 m/s, respectively. The determined elastic modulus and Debye temperature are presented in Table 2 together with those obtained by density functional theory) calculations [33]. The shear modulus, Young’s modulus, bulk modulus, Poisson’s ratio, and Debye temperature obtained in the present study nearly agreed with the theoretically calculated values [33]. In Table 2, the elastic modulus of U₃Si₂ is shown together with the previously reported UO₂ and UN data [28,34,35]. The elastic modulus of U₃Si₂ was lower than that of UO₂ and UN.

The heat capacity of U₃Si₂, as measured by DSC, is shown in Figure 7(a). An empirical equation for the heat capacity of U₃Si₂ can be represented as follows:

Figure 7. (a) Specific heat capacity of U₃Si₂ as a function of temperature. (b) Calculation of specific heat capacity together with experimental data. The highlighted lines indicate the mechanisms that contribute to the ultimate value.

(15) $C{ }_{\mathrm{p}}=100.27+0.07T-2.53\times {10}^{-5}{T}^2$(15)

The experimental values measured in the present study disagreed with the experimental data of Knacke et al. and White et al. over the entire temperature range [7,16]. In addition, the data of Taylor et al. were higher than those reported by the other groups [15]. The reasons for the discrepancies are unclear, since the porosity and impurities will not significantly affect the specific heat capacity. However, we believe our data are more reliable because they are in better agreement with theoretically estimated values, as discussed below.

The theoretically calculated heat capacity is shown in Figure 7(b) together with the experimental data. The heat capacity is commonly composed of dilation, lattice, and electronic components. Heat capacity at constant pressure, C_p, is calculated by [26]:

(16) $C_{\mathrm{p}}=C_{\mathrm{e}}+C_{\mathrm{d}}+C_{\mathrm{v}}$(16)

where C_e is the electronic term, C_d is the dilation term, and C_v is the harmonic lattice vibration term. The dilation term is expressed as:

(17) $C_{\mathrm{d}}=\left(\frac{{\beta }^{2}V}{K_{\mathrm{T}}}\right)\cdot T$(17)

where β is the volumetric expansion coefficient (the value measured by the dilatometer was used here), V is the molar volume, and K_T is the isothermal compressibility which was calculated from the bulk modulus, B, using the following relationship, K_T = 1/B. The electronic term of heat capacity for metallic materials can be expressed as:

(18) $C_{\mathrm{e}}=\eta T$(18)

where η is the electronic specific heat coefficient. White et al. used 52.0 mJ/mol·K² [7] for the η value of U₃Si₂. The harmonic lattice vibration term is expressed using the Debye temperature as follows:

(19) $C_v=9{\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}\left(\frac{T}{{\theta }_{\mathrm{D}}}\right){\int }_0^{{\theta }_{\mathrm{D}}/T}\frac{x^4{\mathrm{e}}^{\mathrm{x}}}{{({\mathrm{e}}^x-1)}^2}dx$(19)

We used the data obtained in this study for θ_D. The summation of C_v, C_e, and C_d components of heat capacity produces the total heat capacity, C_p, shown as the black line in Figure 7(b). The calculated C_v values agreed with the Dulong Petit Law value above the Debye temperature. The calculated data for C_p agreed with the measured values, which indicates that our data are reliable.

From the results of the volumetric thermal expansion (β), bulk modulus (B), and specific heat capacity (C_v), the Grüneisen parameter ($\gamma$) can be calculated as [36]:

(20) $\gamma =\frac{\beta B{V}_m}{C_V}$(20)

where β is the volumetric thermal expansion coefficient of U₃Si₂ (dilatometer), B is the bulk modulus, V_m is the molar volume, and C_v is the calculated lattice vibration heat capacity value at 300 K from Eq. 19(19) $C_v=9{\mathrm{N}}_{\mathrm{A}}{\mathrm{k}}_{\mathrm{B}}\left(\frac{T}{{\theta }_{\mathrm{D}}}\right){\int }_0^{{\theta }_{\mathrm{D}}/T}\frac{x^4{\mathrm{e}}^{\mathrm{x}}}{{({\mathrm{e}}^x-1)}^2}dx$(19) . The calculated data are shown in Table 2 together with those previously determined for UN and UO₂ [37,38]. The Grüneisen parameters of U₃Si₂, UN, and UO₂ are similar, which means that there is no significant difference in the inharmonicity of the bonding in these materials.

The temperature dependence of the thermal diffusivity of U₃Si₂ is shown in Figure 8(a). The thermal conductivities were calculated from the thermal diffusivity measurements using the following relationship:

(21) $\lambda =D\cdot \rho \cdot C_{\mathrm{p}}$(21)

Figure 8. (a) Temperature dependence of the thermal diffusivity. (b) Temperature dependence of the thermal conductivity of U₃Si₂ together with previously reported data. (c) Temperature dependence of the total thermal conductivity, electrical thermal conductivity, and lattice thermal conductivity of U₃Si_2.

where D is the measured thermal diffusivity, ρ is the calculated sample density, and C_p is the specific heat capacity measured using DSC. The temperature dependence of the thermal conductivity of U₃Si₂ is shown in Figure 8(b) along with previously reported values. The thermal conductivity increases with increasing temperature from 6.7 W/mK at 300 K to 19.1 W/mK at 1230 K. The thermal conductivity increases with increasing temperature. Our data, which were obtained from a sintered sample, are close to the value reported [7], which were also obtained from a sintered sample. Shimizu fabricated U₃Si₂ specimens by induction casting and arc casting [17]. Although the thermal conductivity of the arc casted U₃Si₂ agrees well with our data, that of the induction casted U₃Si₂ is much lower, possibly due to cracking. The thermal conductivity of U₃Si₂ was compared with that of UO₂ and UN [39,40]. The thermal conductivity of U₃Si₂ was similar to that of UO₂ at approximately 400 K but is significantly higher than that of UO₂ at temperatures above 500 K since the thermal conductivity of UO₂ decreases with increasing temperature. On the other hand, the thermal conductivity of UN shows the same trend with that of U₃Si₂ as they both increase with temperature [40].

Thermal conduction consists of lattice and electronic contributions. The total thermal conductivity can be represented as follows:

(22) ${\lambda }_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\lambda }_{\mathrm{e}\mathrm{l}\mathrm{e}}+{\lambda }_{\mathrm{l}\mathrm{a}\mathrm{t}}$(22)

where λ_ele is the electronic thermal conductivity, and λ_lat is the lattice thermal conductivity. The value of λ_ele is expressed by the Wiedemann–Franz law [41]:

(23) ${\lambda }_{\mathrm{e}\mathrm{l}\mathrm{e}}=L\cdot \sigma \cdot T$(23)

where L is the Lorenz number (2.45 × 10⁻⁸ W·Ω·K⁻²), and σ is the electrical conductivity. Taylor et al. reported the value of electrical conductivity only at 300 K, which was 6.67 × 10⁵ Sm⁻¹ [14]. The calculated electronic thermal conductivity and lattice thermal conductivity are shown in Figure 8(c). At 300 K, the λ_ele is 4.9 W/mK, which is larger than λ_lat (1.80 W/mK) indicating that electronic contribution is dominant. Since the lattice thermal conductivity tends to decrease with increasing temperature due to the phonon–phonon scattering effect, the electronic contribution is more dominant at higher temperature. Thus, the increase in the temperature-dependent thermal conductivity of U₃Si₂ can largely be ascribed to the electronic contribution.

The hardness, H_V, of the sample was measured by a diamond pyramid type indenter and defined by [42]:

(24) $H_{\mathrm{v}}=0.18544\left(\frac{F}{a^2}\right)$(24)

where F is the applied load, and a is the diagonal average of the indentation. The corresponding indentation fracture toughness, K_IC, of U₃Si₂ can be estimated from the following equation [43]:

(25) $K_{\mathrm{I}\mathrm{C}}=\mathrm{A}{\left(\frac{E}{H}\right)}^{1/2}\left(\frac{P}{c^{3/2}}\right)$(25)

where c is the average length of four cracks generated from the vertex of the indentation, and A is a constant with a value of 0.016. E and H_V are the Young’s modulus and hardness calculated in the present study, respectively. The impressions and cracks in the indents were characterized using FE-SEM and are shown in Figure 9(a). The average diagonal a, c/a ratio, Vickers hardness, and fracture toughness are summarized in Table 3. The Vickers hardness and fracture toughness of U₃Si₂ were found to be 7.51 ± 0.41 GPa and 3.25 ± 0.20 MPa·m^1/2, respectively, which are plotted together with the previously reported values for U₃Si₂, UN, and UO₂ [18,29,44,45] in Figure 9(b, c) as a function of the indentation load. The Vickers hardness value of U₃Si₂ obtained in this study is in good agreement with the literature data reported [18]. Figure 9(b) shows that U₃Si₂ possesses higher hardness than UN and UO₂. In contrast, the fracture toughness for U₃Si₂ obtained in this study is 58% higher than that reported by Metzger et al. (0.86 MPa·m^1/2) [18]. They also reported that USi and U₃Si₅ were present in their U₃Si₂ sample based on EDX analysis. Since precipitates at grain boundaries could deteriorate toughness [46,47], secondary phases such as USi and U₃Si₅ might affect the measured fracture toughness, which would account for the differences between Metzger’s data and those reported herein.

Figure 9. (a) The Vickers indentation fracture pattern of U₃Si₂ at 9.8 N imaged by FE-SEM. (b) Vickers hardness as a function of indentation load for U₃Si₂. (c) Fracture toughness as a function of indentation load for U₃Si_2.

4. Conclusion

A dense U₃Si₂ sample was fabricated, and its thermal and mechanical properties were measured. We successfully synthesized a dense sample with a single phase of U₃Si₂. The average LTEC s determined by HT-XRD and dilatometer were 15.8 ± 1.3 × 10⁻⁶ and 16.4 ± 0.2 × 10⁻⁶ K⁻¹, respectively. The measured specific heat capacity was slightly lower than the literature values, but our data are in good agreement with the theoretical values calculated by the summation of phonon, electron, and volume expansion terms, which indicates our data are reliable. The obtained thermal conductivity was 6.7 W/mK at 300 K, and increases with temperature. At 1230 K, the value reached 19.1 W/mK. The mechanical properties measured in the present study are the first such reported data. The elastic moduli and Debye temperature were evaluated at 300 K, which agreed well with the values obtained by theoretical calculations. The Vickers hardness and fracture toughness of U₃Si₂ were 7.51 ± 0.41 GPa and 3.25 ± 0.20 MPa.m^1/2, respectively, which are higher than those of UO₂. Based on the higher fracture toughness and higher thermal conductivity of U₃Si₂ compared to UO₂, it is expected that U₃Si₂ would be more tolerant to pellet cracking caused by thermal stress.

Disclosure statement

No potential conflict of interest was reported by the authors.