Bala Ji - Academia.edu (original) (raw)

Papers by Bala Ji

Certain materials produce electric charges on their surfaces as a consequence of applying mechani... more Certain materials produce electric charges on their surfaces as a consequence of applying mechanical stress. The induced charges are proportional to the mechanical stress. This is called the direct piezoelectric effect and was discovered in quartz by Piere and Jacques Curie in 1880. Materials showing this phenomenon also conversely have a geometric strain proportional to an applied electric field. This is the converse piezoelectric effect. The root of the word " piezo " means " pressure " ; hence the original meaning of the word piezoelectricity implied " pressure electricity. " Piezoelectricity is extensively utilized in the fabrication of various devices such as transducers, actuators, surface acoustic wave devices, frequency control and so on. In this chapter we describe the piezoelectric materials that are used, and various potential applications of piezoelectric materials. 1-4) Piezoelectric Strain Constant d The magnitude of the induced strain x by an external electric field E is represented by this figure of merit (an important figure of merit for actuator applications): x = d E. (1) Piezoelectric Voltage Constant g The induced electric field E is related to an external stress X through the piezoelectric voltage constant g (an important figure of merit for sensor applications): E = g X. (2) Taking into account the relation, P = d X, we obtain an important relation between g and d: g = d / ε 0 ε. (ε : permittivity) (3) Electromechanical Coupling Factor k The terms, electromechanical coupling factor, energy transmission coefficient, and efficiency are sometimes confused. 5) All are related to the conversion rate between electrical energy and mechanical energy, but their definitions are different. 6) (a) The electromechanical coupling factor k k 2 = (Stored mechanical energy / Input electrical energy) (4) or k 2 = (Stored electrical energy / Input mechanical energy) (5) Let us calculate Eq. (4), when an electric field E is applied to a piezoelectric material. Since the input electrical energy is (1/2) ε 0 ε E 2 per unit volume and the stored mechanical energy per unit volume under zero external stress is given by (1/2) x 2 / s = (1/2) (d E) 2 / s, k 2 can be calculated as Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Certain materials produce electric charges on their surfaces as a consequence of applying mechani... more Certain materials produce electric charges on their surfaces as a consequence of applying mechanical stress. The induced charges are proportional to the mechanical stress. This is called the direct piezoelectric effect and was discovered in quartz by Piere and Jacques Curie in 1880. Materials showing this phenomenon also conversely have a geometric strain proportional to an applied electric field. This is the converse piezoelectric effect. The root of the word " piezo " means " pressure " ; hence the original meaning of the word piezoelectricity implied " pressure electricity. " Piezoelectricity is extensively utilized in the fabrication of various devices such as transducers, actuators, surface acoustic wave devices, frequency control and so on. In this chapter we describe the piezoelectric materials that are used, and various potential applications of piezoelectric materials. 1-4) Piezoelectric Strain Constant d The magnitude of the induced strain x by an external electric field E is represented by this figure of merit (an important figure of merit for actuator applications): x = d E. (1) Piezoelectric Voltage Constant g The induced electric field E is related to an external stress X through the piezoelectric voltage constant g (an important figure of merit for sensor applications): E = g X. (2) Taking into account the relation, P = d X, we obtain an important relation between g and d: g = d / ε 0 ε. (ε : permittivity) (3) Electromechanical Coupling Factor k The terms, electromechanical coupling factor, energy transmission coefficient, and efficiency are sometimes confused. 5) All are related to the conversion rate between electrical energy and mechanical energy, but their definitions are different. 6) (a) The electromechanical coupling factor k k 2 = (Stored mechanical energy / Input electrical energy) (4) or k 2 = (Stored electrical energy / Input mechanical energy) (5) Let us calculate Eq. (4), when an electric field E is applied to a piezoelectric material. Since the input electrical energy is (1/2) ε 0 ε E 2 per unit volume and the stored mechanical energy per unit volume under zero external stress is given by (1/2) x 2 / s = (1/2) (d E) 2 / s, k 2 can be calculated as Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.