Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with monoclinic symmetry

Watt, J. Peter

doi:10.1063/1.327803

Cited by 169 publications

(30 citation statements)

References 10 publications

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“…It is seen that all the Exp. [40] compounds under zero pressure provide the mechanical stability criteria [42][43][44][45][46]. The elastic constants C 11 , C 22 , and C 33 measure the a-, b-, and c-direction resistance to linear compression, respectively.…”

Section: Resultsmentioning

confidence: 99%

Optical, electronic, and elastic properties of some A⁵B⁶C⁷ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation

et al. 2017

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Section: Resultsmentioning

confidence: 99%

Optical, electronic, and elastic properties of some A⁵B⁶C⁷ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation

et al. 2017

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“…Table 2 shows the elastic constants and elastic moduli of the three dioxides. A monoclinic system has thirteen independent elastic constants, and its mechanical stability criteria are as follows [28]: Table 2 meet these criteria, indicating that the three dioxides are mechanically stable.…”

Section: Elastic Propertiesmentioning

confidence: 99%

Elastic properties, hardness, and anisotropy in baddeleyite IVTMO2 (M=Ti, Zr, Hf)

Chen

Liang

et al. 2015

Sci. China Mater.

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and HfO 2 thin films. Other researchers have investigated the transformation from monoclinic phase to tetragonal phase in HfO 2 [5], as well as its mechanical [11], optical, and elastic properties [12]. Even with this range of study, some properties of IVTMO 2 , particularly their mechanical properties, are not well understood . For example, elastic anisotropy in thin films usually leads to microcracks, and differences in thermal expansion between a film and matrix might induce a dropping of the film from the matrix.Zhao et al. [10] reported that bulk ZrO 2 has three crystalline structures at normal pressure: cubic (2300−2680°C), tetragonal (1170−2300°C), and monoclinic (<1170°C). Bulk HfO 2 has only two crystalline structures: tetragonal (1750−2800°C) and monoclinic (<1750°C). The most abundant polymorph of TiO 2 found in nature is rutile, and at room temperature it is stable up to 12 GPa, where it directly converts to the baddeleyite-type (monoclinic) phase [13]. Because m-HfO 2 has a larger bulk modulus than the other two metal dioxides [12], it was expected to have high hardness. The bulk modulus was once thought to be good predictor of hardness. Although it is true that a hard material must have a high modulus [14], it is a common misconception that an incompressible material is a hard one. For example, osmium has only a twentieth the hardness of diamond, though its bulk modulus is comparable to diamond, making it one of the most incompressible materials known.It is now well recognized that high bulk and shear moduli do not guarantee high hardness. Other factors-including high electron density, short bond length, high degree of covalent bonding, and near-isotropic deformation-usually dominate a material's intrinsic hardness [15]. Thus, it is important to thoroughly investigate baddeleyite-type IVTMO 2 (we henceforth refer to these m-MO 2 materials as m-TiO 2 , m-ZrO 2 , and m-HfO 2 ), especially their hardness, elasticity, and anisotropy. To our best knowledge, there are no systemic studies of monoclinic metal dioxides, which are stable at room temperature. In the past decade,In this article, we used plane-wave density functional theory to investigate the elasticity, anisotropy, and minimum thermal conductivities of baddeleyite type IVTMO2 (m-TiO2, m-ZrO2, and m-HfO2). The elastic constants and modulus, Poisson's ratio, hardness, sound speed, Debye temperature, and minimum thermal conductivities at high temperature were calculated. These calculations show that m-MO2 is not superhard, with a hardness range of about 8-13 GPa. Among these materials, m-TiO2 is the hardest, while m-HfO2 is the least hard. Their elastic and plastic anisotropy are given in detail. Moreover, the m-HfO2 thin film is the most likely to develop microcracks during preparation because it has the highest elastic anisotropy. Among the three dioxides, m-HfO2 is the best thermal barrier because it has the lowest thermal conductivity.

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“…The elastic constants of gypsum crystal is given by reference [22] , thus elastic moduli by experiment are as: Gv=26.533GPa; Bv=39.256GPa; Gr=24.808GPa; Br=39.238GPa; E=63.227GPa; μ=0.2315, and the corresponding values of moduli by reference [23] : B=44GPa, G=17GPa, E=45.7GPa, μ=0.33. Bulk modulus B of gypsum by DFT Shear modulus G of gypsum by DFT Young's modulus E of gypsum by DFT Fig.…”

Section: Elastic Modulus Of Monoclinic Gypsum Structurementioning

confidence: 99%

Elastic constants and homogenized moduli of gypsum structure based on Density Functional Theory

Jia¹,

Lin²

2018

Proceedings of the 2017 3rd International Forum on Energy, Environment Science and Materials (IFEESM 2017)

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Abstract. Elastic constants and homogenized properties of gypsum structure were investigated by first-principles method. The gypsum (chemical formula of CaSO4•2H2O) is an evaporite mineral and a kind of hydration product of anhydrite (chemical formula: CaSO4). Elastic constants are calculated based on Density Functional Theory (DFT), which can also contribute to provide information for investigate the anisotropy and mechanical properties of gypsum polycrystals. In addition, based on elastic constants (13 independent constants) of the monoclinic crystal, elastic properties of gypsum polycrystals are obtained. The Young's modulus, shear modulus, bulk modulus and Poisson's ration are derived. Therefore, it is fairly meaningful to study the elastic constants to understand the physical, chemical and mechanical properties of gypsum structure. Elastic constants can be used as the measure criterion of the resistance of a crystal to an externally applied stress. The calculated parameters are in excellent agreement with reference by Huang et al..

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Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with monoclinic symmetry

Cited by 169 publications

References 10 publications

Optical, electronic, and elastic properties of some A⁵B⁶C⁷ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation

Optical, electronic, and elastic properties of some A⁵B⁶C⁷ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation

Elastic properties, hardness, and anisotropy in baddeleyite IVTMO2 (M=Ti, Zr, Hf)

Elastic constants and homogenized moduli of gypsum structure based on Density Functional Theory

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Hashin-Shtrikman bounds on the effective elastic moduli of polycrystals with monoclinic symmetry

Cited by 169 publications

References 10 publications

Optical, electronic, and elastic properties of some A5B6C7ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation

Optical, electronic, and elastic properties of some A5B6C7ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation

Elastic properties, hardness, and anisotropy in baddeleyite IVTMO2 (M=Ti, Zr, Hf)

Elastic constants and homogenized moduli of gypsum structure based on Density Functional Theory

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Product

Resources

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Optical, electronic, and elastic properties of some A⁵B⁶C⁷ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation

Optical, electronic, and elastic properties of some A⁵B⁶C⁷ferroelectrics (A=Sb, Bi; B=S, Se; C=I, Br, Cl): First principle calculation