KR100884719B1 - Composition of lead-free ceramics for piezoelectric actuators - Google Patents
Composition of lead-free ceramics for piezoelectric actuators Download PDFInfo
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Abstract
본 발명은 압전 변위 제어용으로 압전 액츄에이터에 사용될 수 있는 높은 전기기계결합계수 및 압전상수와 낮은 소결온도를 갖으며, 특히 납이 함유되지 않은 압전 액츄에이터용 압전 자기 조성물을 제공하고자 하는 것으로서, 그 압전 자기 조성물은 안정한 페로브스카이트 ABO3 구조를 갖는 (NaxKyLiz)NbO3 + a mol% Li2CO3 이며, 0.44<X<0.52, 0.42<Y<0.5, 0.05<Z<0.07, 0<a<0.02 이다. 이에 따라, 소결 온도가 950℃ 이하에서도 압전 특성이 우수하여 적층형 압전 액츄에이터, 압전 변압기 및 초음파 진동자, 착화소자와 같은 고신뢰성 압전부품을 제조할 수 있으며, 또한, 소성 온도가 종래의 압전 세라믹스보다 낮은 온도 조건에서 제조가 가능하여 적층형 압전부품에 응용할 경우 팔라듐(Pd, palladium) 함량을 줄일 수 있어, 보다 값이 저렴한 전극 재료를 이용할 수 있어서 경제적이며, 특히 납을 함유하지 않은 조성으로써 납으로 인한 환경 오염을 감소시킬 수 있는 효과도 있다.The present invention is to provide a piezoelectric ceramic composition having a high electromechanical coupling coefficient and a piezoelectric constant which can be used in a piezoelectric actuator for controlling piezoelectric displacement and a low sintering temperature, and in particular, a lead-free piezoelectric actuator. The composition is a (Na x K y Li z ) NbO 3 + a mol% Li 2 CO 3 having a stable perovskite ABO 3 structure 0.44 <X <0.52, 0.42 <Y <0.5, 0.05 <Z <0.07, 0 <a <0.02. As a result, the piezoelectric properties are excellent even at a sintering temperature of 950 ° C. or lower, whereby a highly reliable piezoelectric component such as a laminated piezoelectric actuator, a piezoelectric transformer, an ultrasonic vibrator and an ignition element can be manufactured, and the firing temperature is lower than that of conventional piezoelectric ceramics. It can be manufactured under temperature conditions, and can be applied to laminated piezoelectric parts to reduce the content of palladium (Pd, palladium), and it is economical to use cheaper electrode materials. It also has the effect of reducing contamination.
압전 액츄에이터 무연 압전 자기 조성물 Piezoelectric Actuator Lead Free Piezoelectric Magnetic Composition
Description
본 발명은 적층형 압전 액츄에이터용 압전 자기 조성물에 관한 것으로서, 특히 압전 변위 제어용으로 적층형 압전 액츄에이터에 사용될 수 있는 높은 전기기계결합계수 및 압전상수와 낮은 소결온도를 갖는 적층형 압전 액츄에이터용 무연 압전 자기 조성물에 관한 것이다.BACKGROUND OF THE
최근 정밀 기계산업과 정보산업의 발달에 따라 미소변위를 제어하거나 진동을 제어하는 압전 액츄에이터가 정밀광학기기, 반도체 장비, 기체유량제어 펌프, 밸브 등에 폭 넓게 응용되고 있다. 이는 종래의 기계식 구동소자에 비하여 압전 액츄에이터가 소형화 및 정밀제어가 가능하며, 응답속도가 빠른 장점이 있기 때문이다.Recently, with the development of the precision machinery industry and the information industry, piezoelectric actuators for controlling micro displacement or vibration are widely applied to precision optical devices, semiconductor equipment, gas flow control pumps, and valves. This is because the piezoelectric actuator can be miniaturized and precisely controlled, and the response speed is faster than the conventional mechanical driving device.
따라서 메카트로닉스의 발전과 더불어 미소변위 제어 부품은 종래의 스텝모터를 이용하는 방식에서 압전 액츄에이터를 이용하는 방식으로 전환될 것이다. 압전 세라믹스를 이용한 압전 액츄에이터 응용에 있어서, 고변위를 발생시키는 재료 가 필요한 실정이다. 압전체의 변형율 S는 압전체에 인가된 전계 E와 압전상수 d33의 관계로 나타낼 수 있으며, 다음과 같은 수식으로 표현된다.Therefore, with the development of mechatronics, the microdisplacement control component will be switched from the conventional step motor method to the piezoelectric actuator method. In piezoelectric actuator applications using piezoelectric ceramics, a material that generates high displacement is required. The strain S of the piezoelectric body can be expressed by the relationship between the electric field E applied to the piezoelectric body and the piezoelectric constant d 33 , and is expressed by the following formula.
----------------------- (1) ----------------------- (One)
액츄에이터의 변위량(S)은 압전상수(d33) 및 전계(E)에 비례하므로, 압전체의 큰 변위량(S)을 얻기 위해서는 높은 압전 상수(d33) 및 전계(E)가 요구된다. 또한, 변위량(S)은 압전재료의 두께(T)에 비례하고, 큰 변위량(S)을 얻기 위한 압전재료의 두께 증가는 높은 인가전압(E)이 요구된다. 이는 소형화 및 정밀제어 시스템의 회로구성상 바람직하지 않다. 따라서 소비 전력 및 발열량이 적고 응답성도 양호함과 동시에 적층수에 따라 변형량을 조절할 수 있으며, 높은 발생력도 가능한 적층형 압전 액츄에이터가 요구되고 있는 실정이다.Amount of displacement (S) of the actuator is proportional to the piezoelectric constant (d 33) and electric field (E), a high piezoelectric constant (d 33) and electric field (E) is required in order to obtain a large displacement amount (S) of the piezoelectric body. In addition, the displacement amount S is proportional to the thickness T of the piezoelectric material, and the increase in the thickness of the piezoelectric material for obtaining the large displacement amount S requires a high applied voltage E. This is undesirable due to the miniaturization and circuit configuration of the precision control system. Therefore, there is a need for a multilayer piezoelectric actuator that can reduce power consumption and heat generation, have good response, and can adjust the deformation amount according to the number of stacked layers, and can also generate high power.
또한, 자기 조성물을 살펴보면 비납계 압전 세라믹스 중 (Na0 .5K0 .5)NbO3은 높은 상전이온도, 낮은 항전계, 높은 잔류분극들의 특성을 가지고 있어 납을 기본조성으로 하는 압전 세라믹스를 대체할 수 있는 대표적인 물질중의 하나로 여겨지고 있다.In addition, the look of the ceramic composition non-lead piezoelectric ceramic (Na 0 .5 0 .5 K) NbO 3 replaces the piezoelectric ceramic of a lead to a basic composition it has the characteristics of high phase transition temperature, a low coercive field, high remnant polarization It is considered one of the representative materials that can be.
그러나 원료 물질들의 높은 흡습성과 소결 중의 휘발로 인하여 일반 통상적 인 소결 방법으로는 높은 특성을 지닌 소결체를 제조하기가 어려운 것으로 알려져 있다.However, due to the high hygroscopicity of the raw materials and volatilization during sintering, it is known that it is difficult to manufacture a sintered body having high properties by a general conventional sintering method.
따라서 지금까지는 Hot Press, Spark Plasma Sintering 등과 같은 고가의 제조공정을 이용하여 소결하였다. 즉, 보다 경제적인 소결법을 강구해야 하는 당위성이 있다. 또한 환경오염, 가격 경쟁력 문제점을 해결하기 위한 방법으로 납산화물 압전 세라믹스를 대처하기 위해서는 이미 알려져 있는 비납계 압전 세라믹스 보다 우수한 유전 및 압전특성이 요구되고 있다.Therefore, until now, sintering was carried out using expensive manufacturing processes such as hot press and spark plasma sintering. That is, there is a need to seek a more economical sintering method. In addition, in order to solve the environmental pollution and price competitiveness problems, better dielectric and piezoelectric properties are required than the known lead-free piezoelectric ceramics to cope with lead oxide piezoelectric ceramics.
이에 의해, 압전 변위 제어용으로 적층형 압전 액츄에이터에 사용될 수 있는 높은 전기기계결합계수 및 압전상수와 낮은 소결온도를 갖는 적층형 압전 액츄에이터용 무연 압전 자기 조성물을 제공하고자 한다.Accordingly, an object of the present invention is to provide a lead-free piezoelectric ceramic composition for a laminated piezoelectric actuator having a high electromechanical coupling coefficient and a piezoelectric constant and a low sintering temperature, which can be used in a laminated piezoelectric actuator for piezoelectric displacement control.
상술한 바와 같은 과제 해결을 위해 본 발명은 Na2CO3, K2CO3, Li2CO3 및 Nb2O5를 원료로 하여 ABO3 구조를 갖는 페로브스카이트 분말인 (NaxKyLiz)NbO3을 합성한 후, 소결 조제 Li2CO3를 첨가하여 (NaxKyLiz)NbO3 + a mol% Li2CO3의 조성을 갖는 것을 특징으로 하는 압전 액츄에이터용 압전 자기 조성물을 기술적 요지로 한다.In order to solve the problems described above, the present invention is a perovskite powder having an ABO 3 structure using Na 2 CO 3 , K 2 CO 3 , Li 2 CO 3 and Nb 2 O 5 as a raw material (Na x K y After the synthesis of Li z ) NbO 3 , a sintering aid Li 2 CO 3 is added to have a composition of (Na x K y Li z ) NbO 3 + a mol% Li 2 CO 3 . To be a technical point.
여기에서, x,y,z 및 a는 0.44<X<0.52, 0.42<Y<0.5, 0.05<Z<0.07, 0<a<0.02 의 범위의 값을 각각 갖는 것이 바람직하며, 조성물 제조 공정 중 하소 온도는 800~900℃, 소결 온도는 900~1100℃인 것이 바람직하다.Here, x, y, z and a preferably have values in the range of 0.44 <X <0.52, 0.42 <Y <0.5, 0.05 <Z <0.07, 0 <a <0.02, respectively, It is preferable that temperature is 800-900 degreeC, and sintering temperature is 900-1100 degreeC.
상기 과제 해결 수단에 의해, 본 발명에 따른 적층형 압전 액츄에이터용 압전 자기 조성물은 소결 온도가 950℃ 이하에서도 압전 특성이 우수하여 적층형 압전 액츄에이터, 압전 변압기 및 초음파 진동자, 착화소자와 같은 고신뢰성 압전부품을 제조할 수 있는 효과가 있다. 또한, 소성 온도가 종래의 압전 세라믹스보다 낮은 온도 조건에서 제조가 가능하여 적층형 압전부품에 응용할 경우 팔라듐(Pd, palladium) 함량을 감소시킬 수 있어, 보다 값이 저렴한 전극재료를 이용할 수 있어서 경제적이며, 특히 납을 함유하지 않은 조성으로써 납으로 인한 환경 오염을 감소시킬 수 있는 효과도 있다.By the above problem solving means, the piezoelectric ceramic composition for laminated piezoelectric actuator according to the present invention has excellent piezoelectric properties even at a sintering temperature of 950 ° C. or lower, thereby providing a highly reliable piezoelectric component such as a laminated piezoelectric actuator, a piezoelectric transformer, an ultrasonic vibrator, and an ignition element. There is an effect that can be produced. In addition, since the firing temperature can be manufactured at a temperature lower than that of conventional piezoelectric ceramics, when applied to a laminated piezoelectric component, the content of palladium (Pd, palladium) can be reduced, so that an inexpensive electrode material can be used. In particular, the composition does not contain lead, which can reduce the environmental pollution caused by lead.
본 발명에 따른 적층형 압전 액츄에이터용 압전 자기 조성물은, 압전 자기 조성물은 안정한 페로브스카이트 ABO3 구조를 갖는 (NaxKyLiz)NbO3 + a mol% Li2CO3 이며, 0.44<X<0.52, 0.42<Y<0.5, 0.05<Z<0.07, 0<a<0.02 의 조성을 갖는 점에 그 특징이 있다.In the piezoelectric ceramic composition for laminated piezoelectric actuators according to the present invention, the piezoelectric ceramic composition has a (Na x K y Li z ) NbO 3 + a mol% Li 2 CO 3 having a stable perovskite ABO 3 structure. It is characterized by having a composition of 0.44 <X <0.52, 0.42 <Y <0.5, 0.05 <Z <0.07, 0 <a <0.02.
이하 첨부된 도면을 참조하면서 본 발명의 실시예를 상세히 설명한다.Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.
본 발명에 따른 적층형 압전 액츄에이터용 압전 자기 조성물의 제조를 위해, 우선 Na2CO3, K2CO3, Li2CO3, Nb2O5를 원료로 하여 안정한 ABO3 구조를 갖는 페로브스카이트 분말인 (NaxKyLiz)NbO3을 제조한다.In order to manufacture the piezoelectric ceramic composition for a laminated piezoelectric actuator according to the present invention, a perovskite having a stable ABO 3 structure using Na 2 CO 3 , K 2 CO 3 , Li 2 CO 3 , Nb 2 O 5 as a raw material Prepare (Na x K y Li z ) NbO 3 as a powder.
그런 후, Li2CO3를 소결 조제로 첨가하여 최종적으로 (NaxKyLiz)NbO3 + a mol% Li2CO3 의 조성을 갖는 압전 자기 조성물을 제조한다. 여기서, 상기 조성에서 x,y,z 및 a는 바람직하게는 0.44<X<0.52, 0.42<Y<0.5, 0.05<Z<0.07, 0<a<0.02의 범위의 값을 각각 갖는다.Then, Li 2 CO 3 is added as a sintering aid to finally prepare a piezoelectric ceramic composition having a composition of (Na x K y Li z ) NbO 3 + a mol% Li 2 CO 3 . Here, in the composition, x, y, z and a preferably have values in the range of 0.44 <X <0.52, 0.42 <Y <0.5, 0.05 <Z <0.07, 0 <a <0.02, respectively.
이상과 같은 본 발명의 압전 자기 조성물의 제조와 관련하여 설명을 부연해 보기로 한다. 본 발명에서는 종래의 압전 세라믹스가 가지는 높은 소성온도와 낮은 압전상수의 문제점을 개선하기 위하여 (NaxKyLiz)NbO3을 합성함으로써 유전율 및 전기기계결합계수(kp)의 증가와 우수한 압전상수(d33)를 얻었으며, 여기에 Li2CO3을 첨가함으로써 950℃의 낮은 온도에서도 소성이 가능하게 되었다.Description will be made in detail with respect to the production of the piezoelectric ceramic composition of the present invention as described above. In the present invention, in order to improve the problems of high firing temperature and low piezoelectric constant of the conventional piezoelectric ceramics, (Na x K y Li z ) NbO 3 is synthesized to increase the dielectric constant and the electromechanical coupling coefficient (kp) and the excellent piezoelectric constant. (d 33 ) was obtained, and the addition of Li 2 CO 3 allowed firing even at a low temperature of 950 ° C.
도 1a 및 도 1b는 (NaxKyLiz)NbO3의 화학조성과 소결 조제(Li2CO3), 소결온도를 나타낸 표이다. 우선 Na2CO3, K2CO3, Li2CO3, Nb2O5를 출발물질로 (NaxKyLiz)NbO3 조성의 세라믹 분말을 제조하였다. 에탄올과 지르코니아 볼을 이용하여 24시간 분쇄하고 건조한 후, 알루미나 도가니를 이용하여 850℃에서 5시간 동안 하소하였다. 보다 완벽한 상 합성을 위하여 분쇄, 건조, 하소를 두 번 반복하였다.1A and 1B are tables showing the chemical composition of (Na x K y Li z ) NbO 3 , a sintering aid (Li 2 CO 3 ), and a sintering temperature. First, a ceramic powder of (Na x K y Li z ) NbO 3 composition was prepared using Na 2 CO 3 , K 2 CO 3 , Li 2 CO 3 , and Nb 2 O 5 as starting materials. It was ground for 24 hours using ethanol and zirconia balls, dried and calcined at 850 ° C. for 5 hours using an alumina crucible. The grinding, drying and calcination were repeated twice for more complete phase synthesis.
제조된 (NaxKyLiz)NbO3 분말에 소결 조제를 넣지 않은 것은 그대로 분쇄, 건조하여 최종분말을 얻었다. 또한 소결 조제로 Li2CO3를 과잉으로 첨가하여 다시 분쇄, 건조하여 최종분말을 얻었다. 최종분말에 PVA(폴리비닐알콜)를 첨가하여 disk 형태로 성형한 후, 알루미나 도가니를 이용하여 900~1100℃에서 4시간 동안 열처리하였다. 원료분말의 흡습성이 높기 때문에 모든 공정에서 수분과의 접촉을 최대한 억제하였다.The sintering aid was not added to the prepared (Na x K y Li z ) NbO 3 powder as it was, and ground to obtain a final powder. In addition, Li 2 CO 3 was added excessively as a sintering aid, and pulverized and dried again to obtain a final powder. PVA (polyvinyl alcohol) was added to the final powder to form a disk, and then heat-treated at 900 to 1100 ° C. for 4 hours using an alumina crucible. Due to the high hygroscopicity of the raw material powder, contact with water was suppressed as much as possible in all processes.
최종분말 및 소결된 시편을 XRD분석을 통하여 상을 확인하였고, SEM을 이용하여 미세조직을 관찰하였다. 전기적 특성을 측정하기 위하여 1mm 두께로 연마한 시편에 Ag 전극을 도포하여 열처리한 후, 130℃에서 30분간 2.8 kV/cm 직류 전계로 분극처리하였다. 이후, 임피던스 해석기(HP4194A)로 압전 세라믹스의 공진주파 수(fr), 반공진주파수(fa), 정전용량(C), 유전손실(tanδ)을 측정하였고, 압전상수(d33)는 베를린코트 유전상수 미터(Berlincourt d33 meter)를 이용하여 측정하였다. 그리고 면진동 모드 전기기계결합계수(kp)와 유전율(εr)은 각각 다음과 같은 수식을 이용하여 계산하였다.The final powder and the sintered specimens were identified by XRD analysis, and the microstructure was observed using SEM. In order to measure the electrical properties, Ag electrode was applied to the specimen polished to a thickness of 1 mm and heat-treated, and then polarized with a 2.8 kV / cm DC electric field at 130 ° C. for 30 minutes. Then, the resonance frequency (f r ), the anti-resonant frequency (f a ), the capacitance (C), the dielectric loss (tanδ) of the piezoelectric ceramics were measured with an impedance analyzer (HP4194A), and the piezoelectric constant (d 33 ) was measured in Berlin. Measurements were made using a Court dielectric constant meter (Berlincourt d 33 meter). The surface vibration mode electromechanical coupling coefficient (k p ) and dielectric constant (ε r ) were calculated using the following equation.
-------------- (2) -------------- (2)
------------------ (3) ------------------ (3)
여기서, f=fa-fr, C는 1kHz에서의 정전용량, A는 시편의 면적, t는 시편의 두께, ε0는 진공유전율로 8.854 x 10-12F/m이다.Where f = f a -f r , C is the capacitance at 1 kHz, A is the area of the specimen, t is the thickness of the specimen, and ε 0 is the vacuum dielectric constant of 8.854 x 10 -12 F / m.
본 발명의 압전 자기 조성물은 전술한 바와 같이, (NaxKyLiz)NbO3 + a mol% Li2CO3 의 조성을 가지며, 0.44<X<0.52, 0.42<Y<0.5, 0.05<Z<0.07, 0<a<0.02의 범위의 값을 각각 갖는다. 이와 같은 본 발명의 압전 자기 조성물을 900~1100℃에서 소결하였으며, 그 물성을 측정한 결과를 도 2에 나타내었다. 도 2a 및 도 2b는 도 1a 및 도 1b에 나타낸 조성을 갖는 압전 자기 조성물의 유전 및 압전특성을 나타낸 것이다. 도 2a 및 도 2b에서 보는 바와 같이, 본 발명의 압전 자기 조성물은 1000℃ 이하의 낮은 소결 온도에서도 높은 압전특성을 가짐을 알 수 있다.As described above, the piezoelectric ceramic composition of the present invention has a composition of (Na x K y Li z ) NbO 3 + a mol% Li 2 CO 3 , and is 0.44 <X <0.52, 0.42 <Y <0.5, 0.05 <Z < 0.07 and 0 <a <0.02, respectively. The piezoelectric ceramic composition of the present invention was sintered at 900 to 1100 ° C., and the results of measuring the physical properties thereof are shown in FIG. 2. 2A and 2B show dielectric and piezoelectric properties of the piezoelectric ceramic composition having the composition shown in FIGS. 1A and 1B. 2A and 2B, it can be seen that the piezoelectric ceramic composition of the present invention has high piezoelectric characteristics even at a low sintering temperature of 1000 ° C. or lower.
보다 자세히 살펴보기 위하여, 도 3a는 Na/K비율을 변화시켜 Li2CO3를 1 mol% 첨가한 시편의 소결온도에 따른 압전 특성을 나타낸 것이다. 이는 도 1a 및 도 1b와 도 2a 및 도 2b에 나타낸 시편 번호 25번부터 40번까지의 샘플에 대한 결과이다. Na/K비율에 따른 시료는 소결온도가 950℃ 이상인 시료의 값이 비슷하였고, Na의 함량이 0.49, 0.51mol%인 것의 값이 높게 나타났다. 도 3b와 도 3c는 Na/K비율을 변화시켜 Li2CO3를 1 mol% 첨가한 시편의 소결온도에 따른 전기기계결합계수와 유전율을 나타낸 것이다. Na/K비율에 따른 시료는 소결온도가 950℃인 시료의 값이 가장 높게 나타났으며, 그 이상의 온도에서는 감소하였고, Na의 함량이 0.49, 0.51mol%인 것의 값이 높게 나타났다.In order to examine in more detail, Figure 3a shows the piezoelectric properties according to the sintering temperature of the specimen to which 1 mol% Li 2 CO 3 is added by changing the Na / K ratio. This is the result for samples Nos. 25 to 40 shown in FIGS. 1A and 1B and 2A and 2B. The samples according to the Na / K ratio had similar values of the samples having a sintering temperature of 950 ° C. or higher, and the values of 0.49 and 0.51 mol% of Na were high. 3b and 3c show the electromechanical coupling coefficient and dielectric constant according to the sintering temperature of the specimen to which the Na / K ratio was added 1 mol% Li 2 CO 3 . According to the Na / K ratio, the sample having the highest sintering temperature of 950 ° C. showed the highest value, and decreased at the higher temperature. The Na content was 0.49 and 0.51 mol%.
전체적으로 살펴보면 (NaxKyLiz)NbO3 세라믹스에 Li2CO3 을 첨가하면 소결성이 개선되어 전기적 특성이 향상된다. 특히, Li의 함량이 0.06mol% 인 시료가 압전특성이 좋았으며, Li2CO3를 첨가할 시에는 압전상수가 크게 향상되었다. Na의 함량이 0.47mol% 인 시료에 Li2CO3를 1mol% 첨가할 시에는 전기기계결합계수가 크게 향상되었으며, Na의 함량이 0.49mol% 인 시료에 Li2CO3를 1.5mol% 첨가할 시에는 유전율이 크게 향상된 것을 알 수 있었다.Looking at the overall (Na x K y Li z ) NbO 3 ceramics in Li 2 CO 3 Adding sintering improves the electrical properties. In particular, the sample having a Li content of 0.06 mol% had good piezoelectric properties, and the addition of Li 2 CO 3 significantly improved the piezoelectric constant. When added to 1mol% of Li 2 CO 3 in a content of Na of 0.47mol%, the sample was significantly improved the electromechanical coupling factor, is added to 1.5mol% of Li 2 CO 3 in which the content of Na 0.49mol% Sample Poetry showed a significant improvement in permittivity.
도 1a 및 도 1b는 (NaxKyLiz)NbO3의 화학조성과 소결 조제(Li2CO3), 소결온도를 나타낸 표를 나타낸 도.1a and 1b are tables showing the chemical composition of (Na x K y Li z ) NbO 3 , a sintering aid (Li 2 CO 3 ), and a sintering temperature.
도 2a 및 도 2b는 (NaxKyLiz)NbO3의 압전 자기 조성물의 유전 및 압전 특성을 나타낸 표를 나타낸 도.2A and 2B show tables showing dielectric and piezoelectric properties of a piezoelectric ceramic composition of (Na x K y Li z ) NbO 3 ;
도 3의 a, b, c는 각각 Na/K의 비율을 다르게 하여 Li2CO3를 1mol% 첨가 하였을 때, 소결 온도에 따른 압전상수(d33), 전기기계결합계수(kp), 유전상수(εr)의 변화 그래프를 나타낸 도.3 a, b, and c are each a piezoelectric constant (d 33 ), electromechanical coupling coefficient (k p ) according to the sintering temperature when 1 mol% of Li 2 CO 3 is added at a different Na / K ratio Is a graph showing a change graph of a constant ε r .
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