**2. Materials and Methods**

The composition of original soil is listed in Table 1. The soil (200 meshes) and simulated radionuclide Ce4+ (CeO2, Aladdin Industrial Inc., purity ≥ 99.99%)) were mixed with the weight ratio of 9:1. The SHS reaction was prepared according to the following chemical equation [28]:

$$4\text{CuO} + \text{Gd}\_2\text{O}\_3 + 2\text{Ti} = \text{Gd}\_2\text{Ti}\_2\text{O}\_7 + 4\text{Cu} \tag{1}$$

The raw materials of CuO, Gd2O3, and Ti (purity ≥ 99.9 wt.%) were purchased from Aladdin Industrial Inc. (Shanghai, China). Different contents of simulated radioactive soil wastes (0 wt.%, 5 wt.%, 10 wt.%, 15 wt.%, 20 wt.%, 25 wt.%) were mixed with the raw materials of SHS reaction (labelled as Cu-0, Cu-5, Cu-10, Cu-15, Cu-20, and Cu-25, respectively). Pretreatment of powder samples is similar as the previous study [28].


**Table 1.** Soil composition in this study.

The SHS/QP process is shown in Figure 1. The self-propagating combustion reactions were ignited by tungsten wire, which was located at one side with tight contact of the green body and heated by a direct current of about 50 A. The SHS reactants were ignited at high temperature, and the combustion wave automatically propagated to the unreacted region until the reaction's completion. Before densification, the W/Re 5/26 thermocouple was placed in the center of the samples to measure the reaction temperature of Cu-0 to Cu-25 specimens. The unpressurized samples were crushed into fine powders for X-ray diffraction analysis (XRD; X'Pert PRO, PANalytical B.V., Almelo, The Netherlands).

**Figure 1.** Diagrammatic sketch of the self-propagating high-temperature synthesis/quick pressing (SHS/QP) process.

For densification, the ignited sample was compressed by 50 MPa with 60 s dwelling time after proper combustion delay time. The SHS-ed compact sample was cut and polished to characterize the microstructure and elemental distribution using field-emission scanning electron microscopy (FESEM; Zeiss Ultra-55, Oberkochen, Germany) and energy-dispersive X-ray spectroscopy (EDX, ULTRA 55, ZEISS, Oberkochen, Germany). The chemical durability of waste form was tested by the Product Consistency Test (PCT) standard. The concentrations of Na and Si in leachate were determined by inductively coupled plasma (ICP) analysis (iCPA 6500, ThermoFisher, Waltham, MA, USA), while that of Ce was obtained by inductively coupled plasma-mass spectrometry (ICP-MS) analysis using an Agilent 7700× spectrometer (Agilent, Santa Clara, CA, USA). The normalized release rates were calculated as the following formula:

$$NR\_i = \frac{\mathbb{C}\_i \cdot V}{f\_i \cdot S\_A \cdot t} \tag{2}$$

where *Ci* is the concentration of element *i* in the solution, *V* is the volume of the leachate (m3), *SA* is the surface area of powder specimen (m2), *fi* is the mass fraction of element *i* in the sample (wt.%) and *t* is the leaching duration (d). The *SA/V* ratio is about 2000 m−1, which is derived from the standard test method for The Product Consistency Test (ASTM c 1285-02) [32]. In this standard, the waste particles are assumed to be spherical and the average particle diameter is 1.12 × <sup>10</sup>−<sup>4</sup> m for −100 (0.149 mm) to +200 (0.074 mm) meshes particles. Therefore, the average particle area and volume are calculated as 3.90 × <sup>10</sup>−<sup>8</sup> m2 and 7.25 × <sup>10</sup>−<sup>13</sup> m3, respectively. The average particle mass is calculated to be 1.96 × <sup>10</sup>−<sup>6</sup> g. Thus, there are 1 g/1.96 × <sup>10</sup>−<sup>6</sup> g = 5.11 × 105 particles in 1 g powder waste form with −100 to +200 meshes particles. Thus, the total surface area of 1 g powder with −100 to +200 meshes particles is calculated to be 1.99 × <sup>10</sup>−<sup>2</sup> <sup>m</sup>2. As long as the density and particle size of waste form remain comparable during the leaching tests, this parameter will remain at a constant value and doesn't need to be calculated every time.
