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The nitride spinels are of considerable interest. The structural parameters of the nitride spinels have been calculated by first-principles. A semiempirical model for the hardness is employed to predict the hardness of nitride spinels and related compounds. The studies show that the influence of the electronic density, the bond strength, and the ionicity on the hardness of ␥-A 3 N 4 ͑A = C, Si, Ge͒ all decrease monotonously in the order of ␥-C 3 N 4 , ␥-Si 3 N 4 , and ␥-Ge 3 N 4 . The origin of superhardness in the group-IV nitride spinels results mainly from A t N 4 tetrahedral units rather than on A o N 6 octahedral units. The detailed studies of the nitride polymorphs experimentally detected and theoretically proposed indicate that the increasing of coordination cannot always result in the increasing of hardness. It has to be emphasized that the relation between the coordination numbers and hardness has to be applied with care.Superhard materials are of utmost importance in modern science and technology. 1-4 High thermal stability is one of many important properties required for industrial applications of hard and superhard coatings on cutting tools. 4 Silicon nitrides ͑␣-and ␤-Si 3 N 4 ͒ are industrially used as structural ceramics at high temperature because they are stable up to the decomposition temperature of 2000 K. 5 Recently, it was reported that cubic Si 3 N 4 ͑␥-Si 3 N 4 ͒ with a cubic spinel structure could be synthesized at pressures above 15 GPa and temperatures exceeding 2000 K, yet persists metastably in air at an ambient pressure to at least 700 K. 6 This new superhard cubic Si 3 N 4 phase opens considerable industrial scope in materials science. Many theoretical and experimental investigations have focused on the new class of potential superhard nitride materials. 7-16 However, no adequately sized single crystals may be obtained. Therefore theoretical calculations that can provide further details about the atomistic structure and related physical properties are highly desirable. Over the last two decades, in the work of material scientists, the search for hard materials with an intrinsic superhardness has to be simplified to a search for materials with a large bulk modulus 2 or shear modulus. 17 Our recent work 18-20 indicated that the hardness is different from the bulk modulus and shear modulus, and a new method for predicting intrinsic superhardness of ideal crystals was presented. In this Brief Report, we will apply this approach to study the origin of hardness in nitrides spinels and related materials. ␥-A 3 N 4 ͑A = C, Si, Ge, Zr͒ has the cubic spinel structure. In this structure either the C, Ge, Si, or Zr atom is in octahedral coordination with six N atoms ͑denoted as A o ͒ and simultaneously in tetrahedral coordination with four N atoms ͑denoted as A t ͒. In order to calculate the hardness H v , we have carried out a first-principle calculation using both the generalized gradient approximation ͑GGA͒ and the local density approximation ͑LDA͒ approach of density functional theory as imp...

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