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Microscopic Theory of Hardness and Design of Novel Superhard Crystals Int. Journal of Refractory Metals and Hard Materials 33 (2012) 93–106 Contents lists available at SciVerse ScienceDirect Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM Microscopic theory of hardness and design of novel superhard crystals Yongjun Tian ⁎, Bo Xu, Zhisheng Zhao State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao, Hebei 066004, China article info abstract Article history: Hardness can be defined microscopically as the combined resistance of chemical bonds in a material to inden- Received 19 October 2011 tation. The current review presents three most popular microscopic models based on distinct scaling schemes Accepted 18 February 2012 of this resistance, namely the bond resistance, bond strength, and electronegativity models, with key points during employing these microscopic models addressed. These models can be used to estimate the hardness of Keywords: known crystals. More importantly, hardness prediction based on the designed crystal structures becomes Hardness feasible with these models. Consequently, a straightforward and powerful criterion for novel superhard Superhard materials Modeling materials is provided. The current focuses of research on potential superhard materials are also discussed. Chemical bond © 2012 Elsevier Ltd. All rights reserved. Crystal design Contents 1. Introduction ............................................................... 93 2. Microscopic models for hardness prediction ................................................ 94 2.1. Bond resistance model ....................................................... 94 2.2. Bond strength model ....................................................... 96 2.3. Electronegativity model ...................................................... 96 2.4. Some points about microscopic hardness models .......................................... 96 3. Novel superhard crystals ......................................................... 97 3.1. B-C crystals ............................................................ 98 3.2. Carbon allotropes ......................................................... 99 3.3. Transition metal compounds ....................................................100 3.4. Other systems ...........................................................102 4. Perspectives ...............................................................103 Acknowledgements ..............................................................104 References ..................................................................104 1. Introduction indenter, several scales such as the Vickers, Knoop, Brinell, and Rock- well scales have been developed. The most common are the Vickers In 1722, the French scientist R.A.F. de Réaumur coined the term and Knoop scales, whose indenters are a pyramidal-shaped diamonds hardness [1]. Since then, hardness has been used as one of the funda- with a square base and an elongated lozenge base, respectively. Hard- mental mechanical properties of materials. Hardness can be defined ness is measured from the ratio of the indenter force to the associated macroscopically as the ability of a material to resist being scratched indentation area. The deduced hardness usually depends on the or dented by another. Although hardness governs the technological shape of the indenter, loading force and rate, indentation size and applications of numerous materials, it is not as well defined as other time, sample orientation, as well as surface condition. For brittle ma- physical properties [2], especially at the atomic scale. Experimentally, terials or material whose hardness approaches that of diamond, the hardness is accurately characterized by the indentation of a material indentation process is not controlled by plastic deformation alone. using a hard indenter. According to the nature and shape of the The brittle microcracking of the sample and the deformation of the indenter also play roles, leading to hardness changes with different loads [3,4]. For metals and their alloys, hardness is observed to ⁎ Corresponding author. Tel.: +86 335 8057047; fax: +86 335 8074545. increase with decreasing indentation size. Large strain gradients E-mail address: [email protected] (Y. Tian). inherent in small indentations produce geometrically necessary 0263-4368/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmhm.2012.02.021 94 Y. Tian et al. / Int. Journal of Refractory Metals and Hard Materials 33 (2012) 93–106 dislocations, causing enhanced hardening [5]. A reliable hardness hardness characterizes a permanent plastic deformation, it is now could be determined from the asymptotic-hardness region of a well- accepted that hardness does not depend monotonously on bulk mod- controlled indentation process. Hardness values widely vary for differ- ulus or shear modulus according to the simple linear correlation, ent materials, i.e., from tenths of a gigapascal or less for ionic crystals, considering that these elastic moduli correspond to reversible elastic to several gigapascals or less for pure metals, and to tens of gigapascals deformation [30]. Consequently, Chen et al. have proposed a macro- for covalent crystals. As generally accepted by the materials science scopic model of hardness by considering the Pugh's modulus ratio, community, materials with Vickers hardness larger than 40 GPa k=G/B[30]. The parameter k is closely correlated to the brittleness/ are classified as superhard materials [2,6]. Readers can also refer to ductility of materials, as well as highlights a relationship between Ref. [7] for a discussion about definition of superhard/ultrahard and the elastic and plastic properties of pure polycrystalline metals: Brit- how they evolve with times. All as-known superhard compounds are tle materials have high k values, and ductile materials have low ones covalent and polar covalent crystals. [31]. In principle, covalent materials with high hardness are obviously Over the past several decades, a large number of studies have brittle with a larger Pugh modulus ratio. Chen correlated k with hard- been devoted to novel superhard materials for both practical and ness, and a better reliability is reached because k responds to both scientific purposes. One is to synthesize robust materials with desir- material elasticity and plasticity. The Vickers hardness can be calcu- 2 0.585 able properties for modern technologies, and the other is to reveal lated as HV =2(k G) −3, which can be used to predict the the controlling factors that determine the hardness of materials at hardness of a variety of materials [30]. This formula fairly well agrees the microscopic level. Superhard materials are of great importance with experimental data. However, both bulk and shear moduli are in various industry areas, such as wear-resistant coating, abrasives, macroscopic concepts, and the origin of hardness is still not cutting and polishing tools [2,8–10]. Diamond is thus far the hardest completely understood. On the other hand, a direct quantification of known substance (HV =95 GPa) with the highest shear modulus and hardness with microscopic parameters may reveal the fundamental Young's modulus. However, the applicability of diamond is limited factors controlling materials hardness, and provide valuable bases because of its chemical reactivity with ferrous materials and nonre- for pursuing new superhard materials. sistance to oxidation. Cubic boron nitride, the second hardest mate- Some models with different physical considerations have been rial with a diamond structure, can be used to cut ferrous metals. recently proposed to evaluate the intrinsic hardness of ideal crystals However, its hardness is only 66 GPa, or 30% lower than that of dia- with microscopic parameters [32–37]. These models can provide rea- mond. Hence, the syntheses of novel inertial superhard materials sonable results based on crystal structures or parameters from with hardness comparable to or even harder than diamond are high- first principles calculations. Considering that the input parameters ly anticipated. Recent searches for new superhard materials mainly for hardness evaluation are either directly obtained from the crystal focus on two classes of materials. The first class includes light- structure or deduced from the constituent elements, these models element compounds in a B-C-N-O system with short and strong are called “microscopic” models. These microscopic models enable three dimensional (3D) covalent bonds, which are crucial for super- the hardness prediction for covalent, polar covalent, and even ionic hard materials. The experimental syntheses of BCxN, BCx, γB28,B6O crystals based on crystal structures, thus greatly aid the design of [9,11–15], etc., have significantly progressed. The second class con- new superhard materials. However, a satisfying and general descrip- sists of materials formed by light elements (B, C, and N) and heavy tion of hardness for covalent crystals, ionic crystals, and metals still transition metals (TMs) that could introduce a high valence electron eludes materials scientists due to inherent complexities [8,38,39]. density into the corresponding compounds, such as ReB2, OsB2,WB4, The outline of the current review is as follow. First, microscopic PtC, IrN2, OsN2, and PtN2 [16–22]. The high valence electron density models for hardness quantification are presented with a brief discus- enables resistance to elastic and plastic deformations. Although the sion of
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