## 1 Introduction
A very interesting class of materials both from a performance and environmental point of view, which researchers all over the world are looking at with attention, are geopolymers. They are characterised by low environmental impact, due to the raw materials used and the low-temperature processing, as well as by avoiding the use of carbonate-based raw materials, with corresponding CO2 emissions, and expensive chemical reagents. Geopolymers are inorganic materials with an amorphous or semi-crystalline nature consisting of a three-dimensional network of AlO4 and SiO4 tetrahedra. Geopolymerization is produced by a chemical reaction between a cementing component (source of aluminosilicates) and an alkaline activator, such as alkaline hydroxides and salts. For the synthesis of geopolymers, raw materials such as metakaolin, calcined clays, and industrial waste such as fly ash or slags have been used. In particular, when secondary raw materials such as fly ash or slag are used, due to their calcium content it is better to define the obtained material as alkali-activated material, and not as a geopolymer. Therefore, alkali-activated materials with optimized properties can be synthesized depending on many parameters, such as the selection of raw materials, process conditions and Si/Al ratio. According to Si to Al ratios, the repeated units of geopolymeric structures include poly-silate-(-Si-O-Al-), poly-silate-siloxo (-Si-O-Al-O-Si-), poly-silate-disiloxo (-Si-O-Al-O-Si-) and sialate link [23]. Key characteristics of geopolymers make them potential environmentally friendly materials, namely, due to their sustainable fabrication method (exploitation of waste streams or by products and low energy consumption). The synergy between geopolymer industries and waste management is a significant boost to the development of geopolymer technologies providing a feasible pathway for the reduction of pollution and the valorisation of waste. Life cycle assessment studies demonstrate the eco-efficiency and low carbon footprint of this kind of waste-to-production stream [24; 25]. In this paper, pre-treated incinerator bottom ash (IBA) and biochar are studied as geopolymers raw materials, in particular the valorisation of these residues is interesting because these materials can be produced anywhere in the world without territorial limitations. The first, which is an Italian commercial product, is an artificial inert aggregate based on aluminosilicates with a semicrystalline nature constituted by an amorphous fraction and many crystalline phases. It comes from a series of chemical-physical treatments of municipal solid waste incinerators bottom ash. The objective is minimizing waste production by transforming it into a reusable material, the so called \"end of waste\" (EOW). The treatment consists of ageing, sieving and washing. After the process, an inert material with silica-based matrix, rich in iron, calcium and aluminium oxides is obtained. This material can be successfully added in the formulation of cement or ceramic materials as substitute for mineral resources [26; 27; 28; 29; 30; 31] and in geopolymers [32; 33; 34]. Other bottom ashes, different from incinerator ones, but rich in silica and alumina, have been successfully used in the geopolymer formulation, such as bottom ash from a thermal power plant [35], circulating fluidized bed combustion bottom ash [36; 37; 38], bagasse bottom ash [39], lignite bottom ash [40] and OXY-combustion and chemical looping combustion bottom ashes [41]. A novelty of this paper, is the use of a non-conventional aluminosilicate precursor in high percentages (up to 70 wt%) to obtain a porous material, without the addition of a foaming agent. In the literature, H\({}_{2}\)O\({}_{2}\), metallic Al and Si have been used as foaming agents to produce geopolymeric foams with contents of biochar up to 30% [42; 43]. Further, the present paper differs also from [PERSON] et al., where biochar by-product-based geopolymer foams, using silica future without metkaoolin, were obtained [44].