## 1 Introduction  
The radiometric properties of particle aggregates mainly include extinction efficiency, absorption efficiency, scattering efficiency, and asymmetric parameter [1; 2; 3; 4]. It is crucial in numbers of science and engineering disciplines, including coal combustion [5; 6], the concrete aggregate industry [7], atmospheric and environmental sciences, materials engineering [8], plastic photo-thermal therapy [9], and nuclear reactor safety [10]. For example, cosmic dust is a typical type of particle aggregate; its radiometric properties are related to the formation of the universe [11]. During magmatic photo-thermal therapy, AuNP particle aggregates interact with near-infrared (NIR) radiation. Absorption efficiency and scattering efficiency need to be determined accurately so that the therapy uses a proper power rate in case of human tissue damage [9]. The radiometric properties of particle aggregates are fundamentally governed by the macroscopic Maxwell's wave equations (MWEs). The microscopic-level complexity of particle aggregates makes a direct solution for MWEs unfeasible. Effective-medium approximations (EMAs) have been widely used to model the radiometric properties of homogeneous substances [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. The unparalleled simplicity of EMAs leads to a simplified calculation. Even for complex heterogeneous substances, EMAs are still used by treating substances as homogeneous and having a refractive index computedwith a phenomenological mixing rule such as the Lorentz-Lorenz, Bruggeman, and Maxwell-Garnett formulas [23; 24]. [PERSON] and [PERSON] [15] studied the radiometric properties of a slab of compact, pure, spherical particles with EMAs and found that the results agreed closely with measurements. [PERSON] [22] compared a mixture of two materials with generic refractive indices of 1.33 and 1.55 and indicated that conventional EMAs could be improved by freely varying the real and imaginary parts of the refractive index of the mixture, at least when the inclusions had size parameters lower than 0.5. In most cases, using EMAs can lead to acceptable results [15; 25; 26]. However, since an EMA ignores the structure and chemical component distribution inside particle aggregates, it may not be able to predict radiometric properties correctly or accurately for heterogeneous particle aggregates with a complex structure and a chemical component distribution. [PERSON] [27] mentioned \"What is at issue here is not which effective-medium theory is applicable to a given heterogeneous medium, but whether or not any of them are.\"  
For spherical particle aggregates with complex structures, the multi-sphere T-matrix (MSTM) method is used to calculate radiometric properties [15; 22; 28; 29]. The MSTM performs a direct simulation of EM wave propagation in large-scale systems of spheres and considers particle position, size, and chemical components [30; 31]. With the MSTM method, researchers can validate the accuracy of EMAs. [PERSON] [3] used the MSTM to study the effect of the hierarchical structure of particle aggregates on radiometric properties of cometary dust particles; the results showed the importance of the aggregate structure to radiometric properties, and this could not be revealed by EMAs. [PERSON] [32] studied the effect of structure morphology on optical properties of soot aggregates using MSTM; similar to [PERSON]'s results, the aggregate structure had an important influence on the radiometric properties. The chemical component in a particle aggregate is essential to radiometric properties. [PERSON] [19] indicated that the chemical component inhomogeneity was potentially important and needed to receive more attention when the radiometric properties of mineral particles of hematite inclusions are calculated with the MSTM. Realistic morphological black carbon fractal aggregates coated with chemically heterogeneous sulfate were also investigated by [PERSON] [16; 33].