Negative Thermal Expansion (NTE) Metamaterials: A Review of Design, Fabrication, and Applications Devashish Dubey, Anooshe Sadat Mirhakimi, and Mohamed A. Elbestawi Abstract: Most materials expand with temperature increases, causing thermal distortions in precision instruments. NTE materials, which shrink with heating, can reduce overall dimensional changes in structures. These materials, called NTE metamaterials, use engineered architectures to achieve negative thermal expansion. Additive manufacturing enables complex NTE structures. This review discusses NTE metamaterials' design, fabrication, and applications, highlighting their potential in electronics, biomedicine, and aerospace. The article covers various NTE architectures, fabrication methods, and materials used in their production. Keywords: mechanical metamaterials; multimaterial 3D printing; additive manufacturing; laser powder bed fusion; direct energy deposition 1. Introduction: Controlling thermal expansion is critical in industrial applications. NTE materials, which shrink when heated, can counteract thermal expansion in structures. Lakes et al. pioneered NTE metamaterials using structural architecture instead of material properties. These materials, called NTE metamaterials, have engineered architectures that exhibit exotic properties, primarily governed by structure rather than composition. This article reviews NTE metamaterials' design, fabrication, and applications. 2. Design: NTE metamaterials use different designs to achieve negative thermal expansion. Bending-based designs use bimaterial strips with different thermal expansion coefficients (CTE) to create contraction. Stretch-based designs use structures that stretch or compress to achieve NTE. Various designs, including bimaterial-strip-based, chirality-based, re-entrant, and others, have been proposed. These designs can be classified as bending or stretch-based, with sub-classifications. 3. Fabrication: NTE metamaterials can be fabricated using additive manufacturing techniques like laser powder bed fusion (LPBF) and direct energy deposition (DED). These methods allow the production of complex structures. LPBF and DED are promising for NTE metamaterials due to their ability to fabricate multimaterial components. Other fabrication methods, including conventional manufacturing techniques like casting, forging, and machining, are also used to produce NTE structures. 4. Material Selection: NTE metamaterials require a significant difference in CTE between constituent materials and a strong interface between them. Materials like aluminium and invar are used for their low CTE values. The bond strength at the interface is crucial for NTE performance. Phase equilibrium diagrams help evaluate the compatibility of different metals and alloys. 5. Conclusion: NTE metamaterials have potential applications in various industries due to their ability to control thermal expansion. Additive manufacturing techniques like LPBF and DED enable the production of complex NTE structures. The review highlights the importance of design, fabrication, and material selection in achieving NTE performance. Future research should focus on optimizingNegative Thermal Expansion (NTE) Metamaterials: A Review of Design, Fabrication, and Applications Devashish Dubey, Anooshe Sadat Mirhakimi, and Mohamed A. Elbestawi Abstract: Most materials expand with temperature increases, causing thermal distortions in precision instruments. NTE materials, which shrink with heating, can reduce overall dimensional changes in structures. These materials, called NTE metamaterials, use engineered architectures to achieve negative thermal expansion. Additive manufacturing enables complex NTE structures. This review discusses NTE metamaterials' design, fabrication, and applications, highlighting their potential in electronics, biomedicine, and aerospace. The article covers various NTE architectures, fabrication methods, and materials used in their production. Keywords: mechanical metamaterials; multimaterial 3D printing; additive manufacturing; laser powder bed fusion; direct energy deposition 1. Introduction: Controlling thermal expansion is critical in industrial applications. NTE materials, which shrink when heated, can counteract thermal expansion in structures. Lakes et al. pioneered NTE metamaterials using structural architecture instead of material properties. These materials, called NTE metamaterials, have engineered architectures that exhibit exotic properties, primarily governed by structure rather than composition. This article reviews NTE metamaterials' design, fabrication, and applications. 2. Design: NTE metamaterials use different designs to achieve negative thermal expansion. Bending-based designs use bimaterial strips with different thermal expansion coefficients (CTE) to create contraction. Stretch-based designs use structures that stretch or compress to achieve NTE. Various designs, including bimaterial-strip-based, chirality-based, re-entrant, and others, have been proposed. These designs can be classified as bending or stretch-based, with sub-classifications. 3. Fabrication: NTE metamaterials can be fabricated using additive manufacturing techniques like laser powder bed fusion (LPBF) and direct energy deposition (DED). These methods allow the production of complex structures. LPBF and DED are promising for NTE metamaterials due to their ability to fabricate multimaterial components. Other fabrication methods, including conventional manufacturing techniques like casting, forging, and machining, are also used to produce NTE structures. 4. Material Selection: NTE metamaterials require a significant difference in CTE between constituent materials and a strong interface between them. Materials like aluminium and invar are used for their low CTE values. The bond strength at the interface is crucial for NTE performance. Phase equilibrium diagrams help evaluate the compatibility of different metals and alloys. 5. Conclusion: NTE metamaterials have potential applications in various industries due to their ability to control thermal expansion. Additive manufacturing techniques like LPBF and DED enable the production of complex NTE structures. The review highlights the importance of design, fabrication, and material selection in achieving NTE performance. Future research should focus on optimizing