The complete piezoelectric tensor has been measured or calculated for only a small subset of potential piezoelectric materials. In particular, the piezoelectric strain constants can be expressed thermodynamically as 1 d k i j T = ( ∂ ε i j ∂ E k ) σ, T = ( ∂ D k ∂ σ i j ) E, T. These can be readily related to the constants e ijk if the elastic compliances s l m j k E T (at constant electric field and temperature) of the materials are known 4: d i j k T = e i l m s l m j k E T. We note that the most commonly used piezoelectric constants appearing in the (experimental) literature are the piezoelectric strain constants, usually denoted by d ijk. The Voigt-notation will be explained below in more detail. In this work, Voigt-notation is employed for brevity so that the relations for the piezoelectric constants read e i j T = ( ∂ D i ∂ ε j ) E, T = − ( ∂ σ j ∂ E i ) ε, T. Of particular interest to this work are the isothermal piezoelectric stress constants (abbreviated in the rest of this paper as simply piezoelectric constants), defined in full tensor notation as e i j k T = ( ∂ D i ∂ ε j k ) E, T = − ( ∂ σ j k ∂ E i ) ε, T, where D, E, ε, σ and T represent the electric displacement field, the electric field, the strain tensor, the stress tensor and the temperature, respectively. The piezoelectric response of a material can be described using different piezoelectric constants, reflecting various derivatives of thermodynamic functions. 1) 1 conveniently describes how mechanical and electrical properties of solids are related. This tensor describes the response of any piezoelectric bulk material, when subjected to an electric field or a mechanical load. The mathematical description of piezoelectricity relates the strain (or stress) to the electric field via a third order tensor. These technologies all rely on the conversion of voltage to mechanical deformation or vice versa. Examples are found in high voltage and power applications, actuators, sensors, motors, atomic force microscopes, energy harvesting devices and medical applications. Today, piezoelectric materials are integral to numerous applications and devices that exploit this effect, and form the basis for a multi-billion dollar worldwide market 2, 3. Conversely, the indirect piezoelectric effect refers to the case when a strain is generated in a material upon the application of an electric field 1. This is often referred to as the direct piezoelectric effect. Piezoelectricity is a reversible physical process that occurs in some materials whereby an electric dipole moment is generated upon the application of a stress. In addition, the ways in which the database can be accessed and applied in materials development efforts are described. The details of the calculations are also presented, along with a description of the format of the database developed to make these computational results publicly available. The results are compared to select experimental data to establish the accuracy of the calculated properties. In this work we employ first-principles calculations based on density functional perturbation theory to compute the piezoelectric tensors for nearly a thousand compounds, thereby increasing the available data for this property by more than an order of magnitude. Despite the technological importance of this class of materials, for only a small fraction of all inorganic compounds which display compatible crystallographic symmetry, has piezoelectricity been characterized experimentally or computationally. Piezoelectric materials are used in numerous applications requiring a coupling between electrical fields and mechanical strain.
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