Showing papers on "Piezoelectricity published in 2004"
TL;DR: A lead-free piezoelectric ceramic with an electric-field-induced strain comparable to typical actuator-grade PZT is reported, achieved through the combination of the discovery of a morphotropic phase boundary in an alkaline niobate-based perovskite solid solution, and the development of a processing route leading to highly textured polycrystals.
Abstract: Lead has recently been expelled from many commercial applications and materials (for example, from solder, glass and pottery glaze) owing to concerns regarding its toxicity. Lead zirconium titanate (PZT) ceramics are high-performance piezoelectric materials, which are widely used in sensors, actuators and other electronic devices; they contain more than 60 weight per cent lead. Although there has been a concerted effort to develop lead-free piezoelectric ceramics, no effective alternative to PZT has yet been found. Here we report a lead-free piezoelectric ceramic with an electric-field-induced strain comparable to typical actuator-grade PZT. We achieved this through the combination of the discovery of a morphotropic phase boundary in an alkaline niobate-based perovskite solid solution, and the development of a processing route leading to highly textured polycrystals. The ceramic exhibits a piezoelectric constant d33 (the induced charge per unit force applied in the same direction) of above 300 picocoulombs per newton (pC N(-1)), and texturing the material leads to a peak d33 of 416 pC N(-1). The textured material also exhibits temperature-independent field-induced strain characteristics.
4,689 citations
TL;DR: In this article, the authors reviewed the literature in this field, with an emphasis on the factors that impact the magnitude of the available piezoelectric response for non-ferroelectric materials such as ZnO and AlN.
Abstract: Thin film piezoelectric materials offer a number of advantages in microelectromechanical systems (MEMS), due to the large motions that can be generated, often with low hysteresis, the high available energy densities, as well as high sensitivity sensors with wide dynamic ranges, and low power requirements This paper reviews the literature in this field, with an emphasis on the factors that impact the magnitude of the available piezoelectric response For non-ferroelectric piezoelectrics such as ZnO and AlN, the importance of film orientation is discussed The high available electrical resistivity in AlN, its compatibility with CMOS processing, and its high frequency constant make it especially attractive in resonator applications The higher piezoelectric response available in ferroelectric films enables lower voltage operation of actuators, as well as high sensitivity sensors Among ferroelectric films, the majority of the MEMS sensors and actuators developed have utilized lead zirconate titanate (PZT) films as the transducer Randomly oriented PZT films show piezoelectric e(31, f) coefficients of about - 7 C/m(2) at the morphotropic phase boundary In PZT films, orientation, composition, grain size, defect chemistry, and mechanical boundary conditions all impact the observed piezoelectric coefficients The highest achievable piezoelectric responses can be observed in {001} oriented rhombohedrally-distorted perovskites For a variety of such films, e(31,f) coefficients of - 12 to - 27 C/m(2) have been reported
1,016 citations
TL;DR: In this paper, the authors review and discuss piezoelectric properties of selected lead free compositions in relation to structural and microstructural features as well as extrinsic contributions (domain walls displacement, conductivity) to their electromechanical properties.
Abstract: Lead oxide based ferroelectrics, represented by lead zirconate titanate (Pb(Zr, Ti)O3) or PZT) are the most widely used materials for piezoelectric actuators, sensors and transducers due to their excellent piezoelectric properties. Considering lead toxicity, there is interest in developing piezoelectric materials that are biocompatible and environmentally friendlier. The low density of non-lead based materials can also be an advantage in transducers for underwater and medical imaging due to expected lower acoustical impedance. Another impetus for seeking alternative to lead based compositions is the need for piezoelectric materials for operation at high temperatures. Several classes of materials are now being reconsidered as potentially attractive alternatives to PZT for special applications. The potassium niobate family, KNbO3, exhibits low dielectric constants, large thickness coupling coefficient along certain non-polar directions, and low density, all of which have advantages for high frequency transducer applications. Several compositions belonging to bismuth titanate family, Bi4Ti3O12, such as SrTi4Bi4O15, are promising candidates for high temperature applications. Lead free materials alone (eg. (Na0.5Bi0.5)TiO3) or in solution with PT (BiScO3 – PbTiO3) are also potentially interesting as they combine high piezoelectric activity and, in some cases, relatively high T
c
. For these families of piezoelectric materials, the processing and piezoelectric response under different conditions of pressure, frequency, and temperature are presently much less understood than for the classical lead containing systems. In this presentation we review and discuss piezoelectric properties of selected lead free compositions (principally for members of the potassium niobate family and bismuth titanate layered compounds) in relation to structural and microstructural features as well as extrinsic contributions (domain walls displacement, conductivity) to their electromechanical properties. It is shown that it is possible to obtain remarkably stable piezoelectric response in some compositions, while others exhibit strong dependence of piezoelectric properties on driving field and frequency. Origins of these different behaviours are discussed.
610 citations
01 Jan 2004
TL;DR: In this article, the authors present a model for piezoelectric transducers used in broadband ultrasonic applications, including the combination of Quartz Crystal Microbalance with other techniques.
Abstract: Fundamentals on Piezoelectricity.- Overview of Acoustic-Wave Microsensors.- Models for Piezoelectric Transducers Used in Broadband Ultrasonic Applications.- Models for Resonant Sensors.- Interface Electronic Systems for Broadband Ultrasonic Applications.- Interface Electronic Systems for AT Quartz Crystal Microbalance Sensors.- Modified Piezoelectric Surfaces.- Sonoelectrochemistry.- Chemical Sensors.- Biosensors.- Natural Systems and Machines.- Fundamentals of Electrochemistry.- Viscoelastic Properties of Macromolecules.- Combination of Quartz Crystal Microbalance with other Techniques.- Ultrasonic Systems for Non-Destructive Testing Using Piezoelectric Transducers.- Ultrasonic Hyperthermia.- Data analysis and Interpretation in Bulk Acoustic Wave ? Thickness Shear Mode Sensors.
437 citations
TL;DR: In this article, the effects of amount of BKT on the electrical properties and crystal structure of lead-free piezoelectric ceramics have been studied, and the results showed that incorporated BKT diffuses into the BNT lattice to form a solid solution during sintering, but changes the crystal structure from rhombohedral to tetragonal symmetry at higher BKT amounts.
Abstract: Lead-free piezoelectric ceramics (095−x)(Bi1∕2Na1∕2)TiO3–x(Bi1∕2K1∕2)TiO3–005BaTiO3 (abbreviated as BNT–BKT–BT100x, with x ranged from 0 to 20mol%) have been studied Effects of amount of BKT on the electrical properties and crystal structure were examined BNT–BKT–BT5 ceramics give good performances with piezoelectric constant d33=148pC∕N, electromechanical coupling factor kp=34%, kt=492%, free permittivity e33T∕e0=700, and dissipation factor tanδ=2% at 1kHz Accordingly, the sample shows larger remanent polarization and lower coercive field than 095BNT–005BT ceramics X-ray diffraction analysis shows that incorporated BKT diffuses into the BNT–BT lattice to form a solid solution during sintering, but changes the crystal structure from rhombohedral to tetragonal symmetry at higher BKT amounts
296 citations
TL;DR: Theoretical analyses and experimental observations of the failure and fracture behaviors of piezoelectric materials are presented in this paper, where the theoretical analyses are based on the Stroh formalism.
284 citations
TL;DR: Experimental data on the structural features of nanorings and nanobows formed by bending single-crystal, PSD ZnO nanobelts exclusively support the electrostatic polar charge model as the dominant mechanism for bending.
Abstract: Bending of polar-surface-dominated (PSD) nanobelts of ZnO can be explained by one of two processes: electrostatic neutralization of the dipole moment via deformation (called an electrostatic polar charge model) or imbalances between surface tensions via surface-termination induced stresses. This article presents experimental data on the structural features of nanorings and nanobows formed by bending single-crystal, PSD ZnO nanobelts. Our data exclusively support the electrostatic polar charge model as the dominant mechanism for bending.
259 citations
TL;DR: In this article, BaTiO3 diffuses into the lattice of (Na 0.5K0.5)NbO3 to form a solid solution, in which orthorhombic symmetry changes to tetragonal symmetry at x≈0.06, and cubic symmetry changes at x=0.20 or higher.
Abstract: (Na0.5K0.5)NbO3 with 0–20 mol% BaTiO3 has been prepared following the conventional mixed oxide process. High-density samples were obtained through the addition of BaTiO3 into (Na0.5K0.5)NbO3 because of an increase in grain size. X-ray diffraction analysis revealed that, during sintering, all of the BaTiO3 diffuses into the lattice of (Na0.5K0.5)NbO3 to form a solid solution, in which orthorhombic symmetry changes to tetragonal symmetry at x≈0.06, and tetragonal symmetry changes to cubic symmetry at x=0.20 or higher. It was found that the samples with a low content of BaTiO3 exhibit relatively good ferroelectric and piezoelectric properties. For 0.98(Na0.5K0.5)NbO3-0.02 BaTiO3 ceramics, the remanent polarization (Pr) is 7.5 µC/cm2 with a coercive field (Ec) of 12 kV/cm. The piezoelectric constant d33 reaches 104 pC/N. The electromechanical coupling coefficients of the planar mode kp and the thickness mode kt reach ~29% and ~38%, respectively. Our results show that (Na0.5K0.5)NbO3-BaTiO3 is a good lead-free piezoelectric ceramic.
210 citations
TL;DR: In this article, the piezoelectric effect has been studied in wet and dry human bones using a piezoresponse force microscope (PFM), which allowed to measure the piezelectric response with nanometer scale resolution directly in a collagen matrix and to obtain a piezeoselectric image near the Haversian channel.
Abstract: The piezoelectric effect has been studied in wet and dry human bones using a piezoresponse force microscope (PFM). It allowed to measure piezoelectric response with nanometer scale resolution directly in a collagen matrix and to obtain a piezoresponse image near the Haversian channel. Dielectric response and dc conductivity have been measured. Theoretical calculations taking into account the inhomogeneity of the electric field under the PFM tip apex and its screening in highly conductive bone samples were performed for obtaining the piezoelectric coefficient in the bone collagen.
186 citations
TL;DR: In this paper, the authors measured the temperature dependence of the effective transverse piezoelectric coefficient (e31,f) in lead zirconate titanate (PZT) thin films.
Abstract: The temperature dependence of the effective transverse piezoelectric coefficient (e31,f) in lead zirconate titanate (PZT) thin films was measured between −55 and 85 °C. e31,f was calculated by simultaneously monitoring the piezoelectric charge output and strain in the film during wafer flexure. This method was used to characterize the temperature dependence of e31,f in PZT films with 2, 4, and 6 μm thickness and 40/60, 52/48, and 60/40 Zr/Ti ratios. |e31,f| was found to increase with temperature and average increases were 46%, 32%, and 12% for films with PZT 60/40, 52/48, and 40/60 compositions, respectively. Measurement uncertainty ranged from ±3%–12%. The measured temperature dependences of e31,f were consistent with the rapid rise in intrinsic d31 as Tc is approached, suggesting that they were controlled by intrinsic contributions. Additional contributors to the measured variation in the PZT film piezoelectric response over the measured temperature range were identified. Changes in film elastic propert...
180 citations
TL;DR: In this paper, the microstructure, dielectric and piezoelectric properties of (Bi 1/2 Na 1/ 2 )TiO 3 -6BaTiO3 doped with Nb 5+, Co 3+ or La 3+ were studied for a candidate as lead-free, lead free, lead-resistant, and lead free ceramics.
TL;DR: A magnetoelectric laminate composite consisting of magnetostrictive Terfenol-D (Tb1-xDyxFe2-y) and piezoelectoric Pb(Zr,Ti)O3 layers has an extremely high voltage gain effect of ≈300 at its resonant state, offering potential for high-voltage miniature transformer applications as mentioned in this paper.
Abstract: A magnetoelectric laminate composite consisting of magnetostrictive Terfenol-D (Tb1–xDyxFe2–y) and piezoelectric Pb(Zr,Ti)O3 layers has an extremely high voltage gain effect of ≈300 at its resonant state, offering potential for high-voltage miniature transformer applications.
TL;DR: In this article, a finite element model for the static and dynamic analysis of a piezoelectric bimorph is proposed, which combines a 2D single-layer representation model (finite 2D isoparametric elements) for the mechanical displacement field with a layerwise-like approximation for the electric potential field to achieve the accurate prediction of both mechanical displacement and electric potential fields.
TL;DR: Based on piezoelectric constitutive equations and Bragg law, the authors in this article proposed an extended model to evaluate the residual stress in ferroelectric thin film with X-ray diffraction (XRD).
TL;DR: In this paper, the dielectric and piezoelectric properties of the SPS-sintered NbO 3 samples were investigated and compared to that of hot-pressed samples.
TL;DR: In this paper, single crystals of relaxor PMN-0.32PT were subjected to combined stress, electric field, and thermal loading and the results demonstrate that combinations of stress and electric field drive the phase transformation and that the driving force for this transformation decreases with increasing temperature.
TL;DR: The elastic, piezoelectric, and dielectric constants of 0.58Pb(Mg1/3Nb2/3)O3-0.42PbTiO3 were determined experimentally using combined resonance and ultrasonic methods as mentioned in this paper.
Abstract: The elastic, piezoelectric, and dielectric constants of 0.58Pb(Mg1/3Nb2/3)O3-0.42PbTiO3 (PMN-42%PT) were determined experimentally using combined resonance and ultrasonic methods. At room temperature the PMN-42%PT single crystal has tetragonal symmetry. The measured piezoelectric constant d33 is ∼260×10−12 C/N. The electromechanical coefficients k15, k31, k33, and kt are 0.80, 0.39, 0.78, and 0.62, respectively. From the measured material constants the orientational dependence of phase velocities and electromechanical coupling coefficients was calculated. The results showed the tetragonal crystal exhibits isotropy in the X-Y plane and k15, k33, and kt reach their maxima in [001].
TL;DR: In this article, the resonant frequency change of piezoelectric microcantilevers due to a combination of mass loading and spring constant variation arisen from antigen-antibody interaction of C-reactive protein (CRP).
Abstract: A micromachined PZT (52/48) thin film cantilever composed of SiO2/Ta/Pt/PZT/Pt/SiO2 on a SiNx supporting layer for simultaneous self-exciting and sensing was fabricated. We present the resonant frequency change of piezoelectric microcantilevers due to a combination of mass loading and spring constant variation arisen from antigen-antibody interaction of C-reactive protein (CRP). Experimentally measured resonant frequency shift is larger than that of theoretically calculated resonant frequency by two orders of magnitude due to a compressive stress arising from CRP antigen-antibody interaction. The changes in normalized resonant frequency shift δf expt/f1 expt were found to increase as the value of 40.5, 74.7, and 185×10−4 as the CRP antibody site ratio, increased 10%, 50%, and 100%, respectively.
TL;DR: In this paper, two different electric networks are employed for passive electric damping of structural vibrations by distributed piezoelectric transducers and electric networks, and the experimental results are shown to be in very good agreement with theoretical predictions.
Abstract: The aim of this work is two-fold: to design devices for passive electric damping of structural vibrations by distributed piezoelectric transducers and electric networks, and to experimentally validate the effectiveness of such a damping concept. Two different electric networks are employed, namely a purely resistive network and an inductive–resistive one. The presented devices can be considered as distributed versions of the well-known resistive and resonant shunt of a single piezoelectric transducer. The technical feasibility and damping effectiveness of the proposed novel devices are assessed through the construction of an experimental prototype. Experimental results are shown to be in very good agreement with theoretical predictions. It is proved that the presented technique allows for a substantial reduction in the inductances used when compared with those required by the single resonant shunted transducer. In particular, it is shown that the required inductance decreases when the number of piezoelectric elements is increased. The electric networks are optimized in order to reduce forced vibrations close to the first resonance frequency. Nevertheless, the damping effectiveness for higher modes is experimentally proved. As well as specific results, fundamental theoretical and experimental considerations for passive distributed vibration control are provided.
TL;DR: In this article, a double expansion of cellular polypropylene films through an increase in gas pressure and subsequent pressure release at elevated temperatures prior to charging is known to enhance the piezoelectric d33-coefficient of the material.
Abstract: Expansion of cellular polypropylene films through an increase in gas pressure and subsequent pressure release at elevated temperatures prior to charging is known to enhance the piezoelectric d33-coefficient of the material. By means of a second pressure expansion the piezoelectric activity can be further increased by more than 40% in comparison with samples subjected to only a single expansion. The effectiveness of the double-expansion process must be attributed to the gain in thickness through the second expansion, following the charging and metallization processes. This thickness change causes a decrease in Young's modulus and thus an increase in d33. Typical d33-coefficients of 1400 pC N−1 at 0.01 Hz and about 500 pC N−1 at 25 kHz have been achieved.
TL;DR: In this paper, the authors evaluated the properties of piezoelectric BaTiO 3 barium titanate as the embedded material with magnetostrictive CoFe 2 O 4 cobalt iron oxide as the matrix material.
Abstract: Several researchers have focused on developing material properties for homogeneous magneto-electro-elastic multiphase composite materials. The candidate materials for this study are piezoelectric BaTiO 3 barium titanate as the embedded material with magnetostrictive CoFe 2 O 4 cobalt iron oxide as the matrix material. The materials are evaluated in terms of modeling the physical problem of the free vibration an infinite plate. Multiphase material properties vary depending upon the ratio of fiber material to matrix material. Actual electromagnetic materials are modeled as layered materials with the ratio of constituent materials being controlled by varying the number and thickness of layers of each material. Frequencies of vibration are compared for the layered materials versus the multiphase materials as a measure of the accurateness of the derived material constants. Multiphase material predictions for frequency agree quite well with layered materials for the problem that is studied.
TL;DR: In this article, an experimental investigation of the electromechanical behavior of single crystals of the ferroelectric material barium titanate is presented, where the electrostrictive response is highly dependent on the level of applied stress with a maximum strain of 0.9% measured at a compressive stress of about 2 MPa and electric 8 voltage of about 10 kV/cm.
Abstract: An experimental investigation of the electromechanical behavior of single crystals of the ferroelectric
perovskite barium titanate is presented. An experimental setup has been designed to
investigate large strain actuation in single crystal ferroelectrics subjected to combined electrical
and mechanical loading. Experiments have been performed on initially single domain crystals
of barium titanate with (1 0 0) and (0 0 1) orientation at compressive stresses between 0 and
5 MPa. Global strain and polarization histories have been recorded. The electrostrictive response
is shown to be highly dependent on the level of applied stress with a maximum strain of 0.9%
measured at a compressive stress of about 2 MPa and electric 8eld of about 10 kV/cm. This
level of strain is about 5 times higher than in typical commercial piezoelectric PZT. Polarized
light microscopy has been used to observe the evolution of the domain pattern simultaneously
with the strain and polarization measurement. The observations reveal that the observed large
strain behavior is the result of 90° domain switching.
Book•
01 Jan 2004
TL;DR: In this paper, an electric scanning probe imaging and modification of Ferroelectric Surfaces was used for the analysis of the local piezoelectric response and for the determination of the dielectric properties at inner and outer interfaces in PZT thin films.
Abstract: 1 Electric Scanning Probe Imaging and Modification of Ferroelectric Surfaces.- 2 Challenges in the Analysis of the Local Piezoelectric Response.- 3 Electrical Characterization of Nanoscale Ferroelectric Structures.- 4 Nanoscale Optical Probes of Ferroelectric Materials.- 5 Scanning Nonlinear Dielectric Microscopy for Investigation of Ferroelectric Polarization.- 6 Nanoscale Piezoelectric Phenomena in Epitaxial PZT Thin Films.- 7 Scanning Probe Microscopy of Ferroelectric Domains near Phase Transitions.- 8 Nanodomain Engineering in Ferroelectric Crystals Using High Voltage Atomic Force Microscopy.- 9 Nanoinspection of Dielectric and Polarization Properties at Inner and Outer Interfaces in PZT Thin Films.
TL;DR: In this paper, a finite element formulation for active vibration control of thin plate laminated structures with integrated piezoelectric layers acting as sensors and actuators is presented, based on the Kirchhoff classical laminated theory.
TL;DR: In this article, the frequency dependence of magnetoelectric coupling in bilayers and trilayers of Permendur, a ferromagnetic alloy, and lead zirconate titanate was discussed.
Abstract: Magnetoelectric (ME) interactions in layered structures of magnetostrictive and piezoelectric phases are mediated by mechanical deformation. Here we discuss the frequency dependence of ME coupling in bilayers and trilayers of Permendur, a ferromagnetic alloy, and lead zirconate titanate. Data on ME voltage coefficient versus frequency profiles reveal a giant ME coupling at electromechanical resonance. The maximum voltage coefficient of 90 V/cm Oe is three orders of magnitude higher than low-frequency values. The ME interactions for transverse fields are an order of magnitude stronger than for longitudinal fields. These results are in agreement with theory. The resonance ME effect, therefore, is a novel tool for enhancing the magnetic-to-electric field conversion efficiency in the composites.
TL;DR: In this paper, an increase of the piezoelectric d33-coefficient of the cellular polypropylene films by pressure expansion and stacking of the films was reported.
Abstract: Improvements of the sensitivity of piezoelectric microphones based on charged cellular polymer films are reported. The improvements are achieved by (1) an increase of the piezoelectric d33-coefficient of the cellular polypropylene films by pressure expansion and (2) stacking of the films. Microphones consisting of a single film of such material have sensitivities of about 2 mV/Pa at 1 kHz, independent of size, while for a microphone with five stacked films a sensitivity of 10.5 mV/Pa was measured. The equivalent noise level is about 37 dB(A) for the single-film transducer and 26 dB(A) for the stacked version. Advantages of these new piezoelectric transducers include their simple design, low cost, and small weight, as well as a large range of shapes and sizes possible.
TL;DR: The PZT-based ceramics with a composition of Pb1−0.5x(Zr0.52Ti0.48)1−xNbxO3; x=0.591 as mentioned in this paper.
Abstract: The PZT-based ceramics with a composition of Pb1−0.5x(Zr0.52Ti0.48)1−xNbxO3; x=0.02–0.06 were prepared by conventional mixed-oxide method, with sintering temperature at 1250 °C for 2 h. Microstructural and compositional analyses of the PZT-based ceramics have been carried out using XRD and SEM. The dielectric constant measured at 1 kHz is about 1500 and the loss factor is small than 2%. The maximum planar electromechanical coupling coefficient, kp, is 0.591. It showed that the Nb additives were helpful improve both of the dielectric and piezoelectric properties. Surface acoustic wave (SAW) filters were fabricated and the property, phase velocity, were measured.
TL;DR: In this article, the suitability of piezoelectric aluminium nitride (AlN) films deposited by RF sputtering as the actuating element in microelectromechanical system (MEMS) devices was investigated.
Abstract: In this work we investigate the suitability of piezoelectric aluminium nitride (AlN) films deposited by RF sputtering as the actuating element in microelectromechanical system (MEMS) devices. We have studied the influence of some sputtering parameters (substrate bias voltage and pressure) on the preferred orientation, grain size, residual stress and piezoelectric response of the films. X-ray diffractometry (XRD) has been used to obtain the preferred orientation and grain size. The residual stress was deduced from measurements of wafer curvature. The piezoelectric response was evaluated from the frequency response of surface acoustic wave (SAW) filters. A careful control of the energy supplied to the substrates enabled us to grow films with pure c -axis orientation and good piezoelectric response. The sputtering pressure had to be adjusted to reduce the amount of residual stress. As a result, we have determined the relationship between the sputtering parameters and the film characteristics. We present preliminary results of the fabrication of micromachined suspended bridge structures formed by AlN/polysilicon bimorphs.
TL;DR: It is concluded that a reason that the stiffness of ovum measured in the present study is approximately six times larger than previously reported may be due to the absence of large deformation present in of existing methodologies.
TL;DR: In this article, an experimental investigation of the clamping effect associated with thick-film piezoelectric elements printed on a substrate was carried out, and the experimental results showed a reduction in d33 of 74% from 529pC/N to 139pC /N.
Abstract: This paper details an experimental investigation of the clamping effect associated with thick-film piezoelectric elements printed on a substrate. The clamping effect reduces the measured piezoelectric coefficient, d33, of the film. This reduction is due to the influence of the d31 component in the film when a deformation of the structure occurs, by either the direct or indirect piezoelectric effect. Theoretical analysis shows a reduction in the measured d33 of 62%, i.e. a standard bulk lead zirconate titanate (PZT)-5H sample with a manufacturer specified d33 of 593pC/N would fall to 227.8pC/N. To confirm this effect, the d33 coefficients of five thin bulk PZT-5H samples of 220µm thickness were measured before and after their attachment to a metallized 96% alumina substrate. The experimental results show a reduction in d33 of 74% from 529pC/N to 139pC/N. The theoretical analysis was then applied to existing University of Southampton thick-film devices. It is estimated that the measured d33 value of 131pC/N of the thick-film devices is the equivalent of an unconstrained d33 of 345pC/N.