## 1 Introduction  
It is well known that the properties of materials are closely related to their structures and morphologies [1]. Recently, the controlled synthesis of mesoporous structures has become one of the hotspots in the research of new functional materials [2]. The reason is that the mesoporous structure can provide electron or ion transport channels, more reactive sites, and transport channels of reactants, which makes this structure applied in many important fields [3]. As an important functional material, spinel nickel cobaltite (NiCo\({}_{2}\)O\({}_{4}\)) has been intensively applied in electrochemical and catalytic fields due to its good electronic conductivity, multiple convertible valence state, and excellent electrochemical and catalytic activity [4; 5; 6]. Hence, the fabrication of mesoporous nanostructure of NiCo\({}_{2}\)O\({}_{4}\) has attracted much attention.  
To date, various mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanostructures have been widely investigated and demonstrated significantly improved properties. For example, [PERSON] et al. prepared mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanoparticles by the chemical deposition method and demonstrated their improved electrochemical activity towards urea electro-oxidation [7]. [PERSON] et al. synthesized mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanoparticles via an ascorbic acid-assisted co-precipitation method, which exhibited enhanced lithium storage properties [8]. [PERSON] et al. reported mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanorods grown on reduced graphene oxide sheets as dual-functional electrode material for supercapacitor and electrochemical oxygen evolution reactions [9]. [PERSON] et al. reported a facile two-step method to synthesize mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanorods with improved properties for glucose sensors and supercapacitors [10]. [PERSON] et al. obtained mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanowires by hydrothermal impregnation method using SBA-15 as template. The mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanowires exhibited excellent pseudo capacitance and good cycling stability when used as supercapacitor electrode material [11]. [PERSON] et al. reported a microwave-assisted method to synthesize mesoporousNiCo\({}_{2}\)O\({}_{4}\) microspheres and studied their promising application in asymmetric and symmetric supercapacitors [12]. Despite the considerable progress that has been made, the majority of methods can only prepare specific mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanomaterials, which makes the preparation of mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanomaterials with multi-morphologies complicated and costly. Therefore, it is crucial to find a simple approach to mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanomaterials with multi-morphologies.  
In this work, based on simple solvothermal and subsequent heat treatment, we successfully synthesized mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanoparticles, nanorods, nanowires, and microspheres by adjusting the types of reaction solvents. When used as additives for ammonium perchlorate (AP), these mesoporous NiCo\({}_{2}\)O\({}_{4}\) nanostructures exhibited apparent catalytic activities by accelerating the thermal decomposition of AP.