铌镁酸铅和铌锌酸铅基铁电单晶中声表面波传播特性研究
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摘要
新型弛豫铁电－正常铁电型固溶体单晶在最近十几年中受到了很大的重视。这是由于和传统的压电材料相比较，新型弛豫型铁电单晶铌镁酸铅－钛酸铅(1-x)Pb(Mg_(1/3)Nb_(2/3))O_3-xPbTiO_3（PMN-PT，又简写为PMN-xPT，其中x指晶体中PbTiO_3含量）和铌锌酸铅－钛酸铅(1-x)Pb(Zn_(1/3)Nb_(2/3))O_3-xPbTiO_3（PZN-PT，又简写为PZN-xPT，其中x指晶体中PbTiO_3含量）等表现出良好的压电、介电、光学和声学性能，这种新型晶体在各种机电设备中具有广泛的应用前景，如医学超声换能器，大位移压电驱动器和超声电机等。PMN-PT、PZN-PT等弛豫铁电单晶对于声表面波器件同样是非常有应用前景的压电材料。虽然有研究者测量了个别晶体的SAW相速度，然而并没有对该晶体的声表面波性能进行系统的理论分析。为了未来的潜在应用，我们研究了PMN-PT、PZN-PT及铌镁铟酸铅－钛酸铅(PIN-PMN-PT)系列晶体的声表面波传播特性，希望能对声表面波器件的设计有所帮助。
首先，本论文利用实验已测得的多种组分的[001]c极化PMN-PT弛豫铁电单晶的弹性、介电和压电参数，求解了半无限大条件下的克里斯托夫方程，理论上首先详细讨论了三方相、四方相和处于准同型相界的PMN-PT单晶的声表面波传播特性。分析了晶体具有优异声表面波性能的原因。理论计算结果表明三方相、准同型相界和四方相PMN-PT晶体均具有比较优异的声表面波特性。声表面波相速度都比较小，都具有声表面波机电耦合系数比较大的切型，能流角均明显小于传统压电材料。这些特性将有助于减小声表面波器件尺寸，增加器件工作带宽，降低能量损耗。与其他组分晶体相比，处于准同型相界的PMN-33%PT晶体的声表面波特性最为优异。k2值高达33.46%，同时声表面波相速度不超过1800m/s，能流角小于1.5o。PMN-33%PT单晶具有优异的声表面波机电性能的内部机理是PMN-33%PT单晶处于准同型相界附近，极化后PMN-33%PT晶体内存在三方—四方两相共存区，等效的极性畴对称地靠近极化方向分布形成工程化的畴结构。工程化的畴结构改变了晶体的宏观对称性，产生较大应变。同时畴壁的运动受到抑制，场致应变的回滞很小。对比发现四方相PMN-38%PT晶体的SAW性能略逊色于PMN-33%PT，同时四方相PMN-38%PT晶体的各向异性强于三方相晶体。PMN-PT单晶虽然具有很好的SAW性能，但其不太好的温度稳定性限制了单晶的应用范围。
此外，研究了极化方向和晶体成分变化对PMN-PT晶体声表面波性能的影响。结果表明，组分相同但极化方向不同时，PMN-PT晶体的声表面波性能不同。沿[001]c方向极化和[111]c方向极化的PMN-33%PT晶体的声表面波性能接近但并不相同。这说明在铁电单晶材料中，铁电畴的取向效应在晶体的SAW性能中起重要作用，因此可以通过改变畴的结构和取向来优化铁电单晶的SAW性能。加入铟可以有效的提高弛豫铁电晶体的SAW性能，本论文初步讨论了加入铟对PMN-PT晶体SAW性能的影响。对比0.71PMN-0.29PT晶体对0.26PIN-0.46PMN-0.28PT晶体的声表面波传播特性进行了研究。结果发现，铟的加入在提高晶体稳定性的同时，牺牲了部分SAW性能。但综合来看，[011]c极化0.26PIN-0.46PMN-0.28PT单晶仍具有相对传统压电材料比较优异的SAW性能和较好的温度稳定性。
由于PZN-PT晶体的温度稳定性好于PMN-PT单晶，本论文讨论了接近准同型相界的三方相、远离准同型相界的三方相和四方相PZN-PT晶体的声表面波传播特性。在我们所研究的各种组分的PZN-PT晶体中，接近准同型相界的三方相PZN-7%PT晶体的声表面波性能最好。PZN-8%PT晶体的SAW性能与PZN-7%PT晶体接近。相比其它组分PZN-PT晶体PZN-7%PT和PZN-8%PT单晶具有较好SAW性能的原因是三方相的PZN-PT晶体的自发极化方向为[111]c，当沿[001]c极化后晶体具有工程畴结构。而工程畴组态的单晶具有更高的电学活性，压电性能远远高于其单畴态。而四方相PZN-PT晶体的自发极化方向为[001]c，当沿[001]c极化时晶体为单畴结构。因而沿[001]c极化的PZN-12%PT晶体的声表面波性能低于同样沿[001]c极化的三方相PZN-PT晶体。如PZN-12%PT晶体声表面波k2最大值仅为6.97%，远低于PZN-7%PT(14.3%)、PZN-8%PT(13.8%)和PZN-4.5%PT(12.54%)。组分相同时，沿不同方向极化的PZN-PT晶体的SAW性能同样存在较大差异。沿[011]c方向极化的具有mm2宏观对称性的PZN-7%PT单晶的SAW性能要优于沿[001]c极化的PZN-7%PT单晶。如[011]c极化的PZN-7%PT单晶声表面波k2最大值可达24.16%，远高于[001]c极化的PZN-7%PT单晶。
Relaxor-based ferroelectric single crystals lead magnesium niobate-leadtitanate (1-x)Pb(Mg_(1/3)Nb_(2/3))O_3-xPbTiO_3(PMN-PT) and lead zinc niobate-leadtitanat (1-x)Pb(Zn_(1/3)Nb_(2/3))O_3-xPbTiO_3(PZN-PT) have attracted considerable attentionin the past several years due to theirs excellent piezoelectric, dielectric, optical andacoustical properties compared to traditional piezoelectric materials. Hence, thesecrystals are favored in the next generation electromechanical devices, includingultrasonic transducers, actuators, ultrasonic motors, etc. The PMN-PT and PZN-PTsingle crystals have tremendous potential applied in surface acoustic wave (SAW)devices. SAW velocities of PMN-33%PT have been measured by Choi KH et al.However, there is no report on the literature on the detailed theoretical analysis ofSAW propagation properties for PMN-PT and PZN-PT single crystals. For meeting theplenteously potential application requirements in the future, surface acoustic wavepropagation characteristics of PMN-PT, PZN-PT and lead indium niobate-leadmagnesium niobate-lead titanat (PIN-PMN-PT) crystals are studied in this paper,and results could contribute to the design of SAW devices.
Firstly, using the measured material parameters of PMN-PT relaxor-basedferroelectric single crystals, the SAW propagation characteristics in PMN-PT singlecrystals at rhombohedral, tetragonal and morphotropic phase boundary be governed bythe Christoffel equation with semi-infinite boundary conditions. Reasons whyPMN-PT single crystals have superior SAW performance were analyzed from thecrystal structure. The theoretical results indicate that, the PMN-PT single crystals allhave superior SAW performance at rhombohedral, tetragonal and morphotropic phaseboundary. We found that the PMN-PT have lower phase velocity and higherelectromechanical coupling coefficient compared and small power flow angle (PFA)to traditional piezoelectric materials, which could drastically improve the performanceof SAW devices. The SAW propagation properties of PMN-33%PT single domainsingle crystals poled along [001]care even better than that of the other componentscrystals. For example; the maximumk2value could reach as high as33.46%in thedirection5o canted, SAW phase velocity and power flow angle be less than1800m/sand1.5o, respectively. Components near MPB are the reasons why PMN-PT singlecrystals have superior SAW performance. After poling, rhombohedral phase andtetragonal phase are coexisting in PMN-33%PT single crystals, and engineereddomain configuration are formed, change of the crystals symmetry brings the largertrain. Moreover, the motion of domain wall was inhibited, and strain delay is small. By comparison, SAW properties of tetragonal phase PMN-38%PT single crystal bejust shy of PMN-33%PT. Moreover, the anisotropy of tetragonal phase PMN-38%PTsingle crystal was more significant than rhombohedral phase crystal. AlthoughPMN-PT single crystal has excellent properties, but poor temperature stability limitsits application.
In addition, we also studied influence of polarization direction and ingredientchange on SAW propagation properties in PMN-PT ferroelectric single crystals. Ourresults showed that the same component but different polarization direction, PMN-PTsingle crystals have different SAW performance. SAW propagation properties inPMN-33%PT ferroelectric single crystals poled along [001]cdiffer from those of[111]c. It shows, the SAW properties of ferroelectric single crystals can be optimizedthrough changing crystals structure. The appropriate doping can effectively improvethe SAW properties of relaxor-based ferroelectric single crystals. In this paper theeffects of doping on SAW properties of single crystals were preliminary studied. TheSAW properties of0.26PIN-0.46PMN-0.28PT single crystals were studied bycontrast with0.71PMN-0.29PT single crystals. The study found lead indium niobatedoping can be helpful to enhance the temperature stability, which depresses the SAWperformance of0.26PIN-0.46PMN-0.28PT single crystals. But overall, the SAWpropagation properties of0.26PIN-0.46PMN-0.28PT single crystals poled along [011]care even better than that of the traditional piezoelectric materials.
Because of the PZN-PT single crystals have better temperature stability thanPMN-PT, the we discussed the SAW propagation characteristics in PZN-PT singlecrystals at rhombohedral, tetragonal and near morphotropic phase boundary. We foundthat the SAW propagation properties of PZN-7%PT single crystal are even better thanthat of the other components crystals. The SAW propagation properties of PZN-8%PTsingle crystal are approximate to those of PZN-7%PT. The PZN-7%PT andPZN-8%PT single crystals have superior SAW performance, because spontaneouspolarization direction of rhombohedral PZN-PT single crystal is [111]c, when thePZN-PT single crystals are polarized along [001]c, they have engineered domainconfiguration with better piezoelectric properties than single domain structure.Moreover, the spontaneous polarization direction of tetragonal PZN-PT single crystalis [001]c. After poling along [001]c, the PZN-PT single crystals have single domainstructure, therefore SAW propagation properties of PZN-12%PT single crystal arelower than that of the rhombohedral crystals poled along [001]c. For example; themaximumk2value of PZN-12%PT single crystal only is about6.97%, far below thatof PZN-7%PT, PZN-8%PT and PZN-4.5%PT. In addition, when the same componentbut different polarization direction, PZN-PT single crystals have different SAW performance. The PZN-7%PT ferroelectric single crystals poled along [011]cwithmm2symmetry have better SAW propagation properties than crystals poled along[001]c, such as the maximumk2value of PZN-7%PT poled along [011]ccould reachas high as24.16%, this is far higher that of PZN-7%PT poled along [001]c.
首先，本论文利用实验已测得的多种组分的[001]c极化PMN-PT弛豫铁电单晶的弹性、介电和压电参数，求解了半无限大条件下的克里斯托夫方程，理论上首先详细讨论了三方相、四方相和处于准同型相界的PMN-PT单晶的声表面波传播特性。分析了晶体具有优异声表面波性能的原因。理论计算结果表明三方相、准同型相界和四方相PMN-PT晶体均具有比较优异的声表面波特性。声表面波相速度都比较小，都具有声表面波机电耦合系数比较大的切型，能流角均明显小于传统压电材料。这些特性将有助于减小声表面波器件尺寸，增加器件工作带宽，降低能量损耗。与其他组分晶体相比，处于准同型相界的PMN-33%PT晶体的声表面波特性最为优异。k2值高达33.46%，同时声表面波相速度不超过1800m/s，能流角小于1.5o。PMN-33%PT单晶具有优异的声表面波机电性能的内部机理是PMN-33%PT单晶处于准同型相界附近，极化后PMN-33%PT晶体内存在三方—四方两相共存区，等效的极性畴对称地靠近极化方向分布形成工程化的畴结构。工程化的畴结构改变了晶体的宏观对称性，产生较大应变。同时畴壁的运动受到抑制，场致应变的回滞很小。对比发现四方相PMN-38%PT晶体的SAW性能略逊色于PMN-33%PT，同时四方相PMN-38%PT晶体的各向异性强于三方相晶体。PMN-PT单晶虽然具有很好的SAW性能，但其不太好的温度稳定性限制了单晶的应用范围。
此外，研究了极化方向和晶体成分变化对PMN-PT晶体声表面波性能的影响。结果表明，组分相同但极化方向不同时，PMN-PT晶体的声表面波性能不同。沿[001]c方向极化和[111]c方向极化的PMN-33%PT晶体的声表面波性能接近但并不相同。这说明在铁电单晶材料中，铁电畴的取向效应在晶体的SAW性能中起重要作用，因此可以通过改变畴的结构和取向来优化铁电单晶的SAW性能。加入铟可以有效的提高弛豫铁电晶体的SAW性能，本论文初步讨论了加入铟对PMN-PT晶体SAW性能的影响。对比0.71PMN-0.29PT晶体对0.26PIN-0.46PMN-0.28PT晶体的声表面波传播特性进行了研究。结果发现，铟的加入在提高晶体稳定性的同时，牺牲了部分SAW性能。但综合来看，[011]c极化0.26PIN-0.46PMN-0.28PT单晶仍具有相对传统压电材料比较优异的SAW性能和较好的温度稳定性。
由于PZN-PT晶体的温度稳定性好于PMN-PT单晶，本论文讨论了接近准同型相界的三方相、远离准同型相界的三方相和四方相PZN-PT晶体的声表面波传播特性。在我们所研究的各种组分的PZN-PT晶体中，接近准同型相界的三方相PZN-7%PT晶体的声表面波性能最好。PZN-8%PT晶体的SAW性能与PZN-7%PT晶体接近。相比其它组分PZN-PT晶体PZN-7%PT和PZN-8%PT单晶具有较好SAW性能的原因是三方相的PZN-PT晶体的自发极化方向为[111]c，当沿[001]c极化后晶体具有工程畴结构。而工程畴组态的单晶具有更高的电学活性，压电性能远远高于其单畴态。而四方相PZN-PT晶体的自发极化方向为[001]c，当沿[001]c极化时晶体为单畴结构。因而沿[001]c极化的PZN-12%PT晶体的声表面波性能低于同样沿[001]c极化的三方相PZN-PT晶体。如PZN-12%PT晶体声表面波k2最大值仅为6.97%，远低于PZN-7%PT(14.3%)、PZN-8%PT(13.8%)和PZN-4.5%PT(12.54%)。组分相同时，沿不同方向极化的PZN-PT晶体的SAW性能同样存在较大差异。沿[011]c方向极化的具有mm2宏观对称性的PZN-7%PT单晶的SAW性能要优于沿[001]c极化的PZN-7%PT单晶。如[011]c极化的PZN-7%PT单晶声表面波k2最大值可达24.16%，远高于[001]c极化的PZN-7%PT单晶。
Relaxor-based ferroelectric single crystals lead magnesium niobate-leadtitanate (1-x)Pb(Mg_(1/3)Nb_(2/3))O_3-xPbTiO_3(PMN-PT) and lead zinc niobate-leadtitanat (1-x)Pb(Zn_(1/3)Nb_(2/3))O_3-xPbTiO_3(PZN-PT) have attracted considerable attentionin the past several years due to theirs excellent piezoelectric, dielectric, optical andacoustical properties compared to traditional piezoelectric materials. Hence, thesecrystals are favored in the next generation electromechanical devices, includingultrasonic transducers, actuators, ultrasonic motors, etc. The PMN-PT and PZN-PTsingle crystals have tremendous potential applied in surface acoustic wave (SAW)devices. SAW velocities of PMN-33%PT have been measured by Choi KH et al.However, there is no report on the literature on the detailed theoretical analysis ofSAW propagation properties for PMN-PT and PZN-PT single crystals. For meeting theplenteously potential application requirements in the future, surface acoustic wavepropagation characteristics of PMN-PT, PZN-PT and lead indium niobate-leadmagnesium niobate-lead titanat (PIN-PMN-PT) crystals are studied in this paper,and results could contribute to the design of SAW devices.
Firstly, using the measured material parameters of PMN-PT relaxor-basedferroelectric single crystals, the SAW propagation characteristics in PMN-PT singlecrystals at rhombohedral, tetragonal and morphotropic phase boundary be governed bythe Christoffel equation with semi-infinite boundary conditions. Reasons whyPMN-PT single crystals have superior SAW performance were analyzed from thecrystal structure. The theoretical results indicate that, the PMN-PT single crystals allhave superior SAW performance at rhombohedral, tetragonal and morphotropic phaseboundary. We found that the PMN-PT have lower phase velocity and higherelectromechanical coupling coefficient compared and small power flow angle (PFA)to traditional piezoelectric materials, which could drastically improve the performanceof SAW devices. The SAW propagation properties of PMN-33%PT single domainsingle crystals poled along [001]care even better than that of the other componentscrystals. For example; the maximumk2value could reach as high as33.46%in thedirection5o canted, SAW phase velocity and power flow angle be less than1800m/sand1.5o, respectively. Components near MPB are the reasons why PMN-PT singlecrystals have superior SAW performance. After poling, rhombohedral phase andtetragonal phase are coexisting in PMN-33%PT single crystals, and engineereddomain configuration are formed, change of the crystals symmetry brings the largertrain. Moreover, the motion of domain wall was inhibited, and strain delay is small. By comparison, SAW properties of tetragonal phase PMN-38%PT single crystal bejust shy of PMN-33%PT. Moreover, the anisotropy of tetragonal phase PMN-38%PTsingle crystal was more significant than rhombohedral phase crystal. AlthoughPMN-PT single crystal has excellent properties, but poor temperature stability limitsits application.
In addition, we also studied influence of polarization direction and ingredientchange on SAW propagation properties in PMN-PT ferroelectric single crystals. Ourresults showed that the same component but different polarization direction, PMN-PTsingle crystals have different SAW performance. SAW propagation properties inPMN-33%PT ferroelectric single crystals poled along [001]cdiffer from those of[111]c. It shows, the SAW properties of ferroelectric single crystals can be optimizedthrough changing crystals structure. The appropriate doping can effectively improvethe SAW properties of relaxor-based ferroelectric single crystals. In this paper theeffects of doping on SAW properties of single crystals were preliminary studied. TheSAW properties of0.26PIN-0.46PMN-0.28PT single crystals were studied bycontrast with0.71PMN-0.29PT single crystals. The study found lead indium niobatedoping can be helpful to enhance the temperature stability, which depresses the SAWperformance of0.26PIN-0.46PMN-0.28PT single crystals. But overall, the SAWpropagation properties of0.26PIN-0.46PMN-0.28PT single crystals poled along [011]care even better than that of the traditional piezoelectric materials.
Because of the PZN-PT single crystals have better temperature stability thanPMN-PT, the we discussed the SAW propagation characteristics in PZN-PT singlecrystals at rhombohedral, tetragonal and near morphotropic phase boundary. We foundthat the SAW propagation properties of PZN-7%PT single crystal are even better thanthat of the other components crystals. The SAW propagation properties of PZN-8%PTsingle crystal are approximate to those of PZN-7%PT. The PZN-7%PT andPZN-8%PT single crystals have superior SAW performance, because spontaneouspolarization direction of rhombohedral PZN-PT single crystal is [111]c, when thePZN-PT single crystals are polarized along [001]c, they have engineered domainconfiguration with better piezoelectric properties than single domain structure.Moreover, the spontaneous polarization direction of tetragonal PZN-PT single crystalis [001]c. After poling along [001]c, the PZN-PT single crystals have single domainstructure, therefore SAW propagation properties of PZN-12%PT single crystal arelower than that of the rhombohedral crystals poled along [001]c. For example; themaximumk2value of PZN-12%PT single crystal only is about6.97%, far below thatof PZN-7%PT, PZN-8%PT and PZN-4.5%PT. In addition, when the same componentbut different polarization direction, PZN-PT single crystals have different SAW performance. The PZN-7%PT ferroelectric single crystals poled along [011]cwithmm2symmetry have better SAW propagation properties than crystals poled along[001]c, such as the maximumk2value of PZN-7%PT poled along [011]ccould reachas high as24.16%, this is far higher that of PZN-7%PT poled along [001]c.
引文
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