A Žukauskas

R Vaicekauskas

M S Shur

Colour rendition properties of solid-state lamps

Keywords: 42, 66, Qg, 85, 60, Jb

Colour-rendition properties of solid-state lamps

A Žukauskas, R Vaicekauskas,

Introduction

Solid-state lighting technology, which emerged with the appearance of blue and white lightemitting diodes (LEDs) [START_REF] Nakamura | The Blue Laser Diode: GaN Based Light Emitters and Lasers[END_REF], has a potential to replace inefficient incandescent and discharge-based sources of light [START_REF] Žukauskas | Introduction to Solid-State Lighting[END_REF]. Recent technological advances [START_REF] Krames | Status and future of high-power light-emitting diodes for solid-state lighting[END_REF][START_REF] Mottier | LEDs for Lighting Applications[END_REF] resulted in that LEDs are outperforming conventional lamps in efficiency. Although numerous performance challenges in solid-state lighting still exist [START_REF] Crawford | LEDs for solid-state lighting: Performance challenges and recent advances[END_REF], the 200-lm/W efficiency barrier that was anticipated for 2020 [START_REF] Tsao | Solid-state lighting: Lamps, chips, and materials for tomorrow[END_REF] has been already broken [START_REF] Cree | Cree breaks 200 lumen per watt efficacy barrier[END_REF].

Despite a rapid progress in efficiency, the potential of solid-state lighting technology in delivering illumination with improved control of colour quality is still almost untapped. Solid-state lighting technology employs the principle of injection electroluminescence in semiconductor junctions used directly or in conjunction with either partial or complete conversion in phosphors [START_REF] Žukauskas | Introduction to Solid-State Lighting[END_REF][START_REF] Steigerwald | Illumination with solid state lighting technology[END_REF][START_REF] Schubert | Solid state light sources getting smart[END_REF]. Such an approach suggests high versatility in composing the spectral power distribution (SPD) of a light source and thus in controlling colour quality of illumination [START_REF] Shur | Solid-state lighting: Toward superior illumination[END_REF]. In particular, light sources with SPDs that contain a few narrow-band electroluminescence components became feasible. Such sources may have colour rendition properties that differ from those of common fluorescent lamps, which emit due only to phosphors. New possibilities in engineering the spectrum of light sources offered by solid-state technology highlight the fact that colour quality of illumination comprises at least two colour rendition properties: the ability to make colours appear "natural" (colour fidelity) and the ability to make colours appear "vivid" and easily distinguishable (colour saturation) [START_REF] Rea | Color rendering: A tale of two metrics[END_REF]. In the previousgeneration lighting technology, the latter property was considered as supplementary, since no common lamps with a pronounced colour-saturating ability were available. Consequentially, the only one widely accepted method of rating lamps in colour quality was the colour rendering index (CRI) [START_REF] Cie | Method of measuring and specifying color rendering properties of light sources Publication[END_REF], which ranks them in how "natural" object colours appear when compared to those under reference broad-band illuminants. However when applications of solid-state sources in lighting emerged, subjective rating of illumination provided by clusters composed of direct-emission LEDs was found to be in an obvious conflict with the standard CRI metric [START_REF] Narendran | Color rendering properties of LED light sources Proc[END_REF][START_REF] Shakir | Evaluating white LEDs for outdoor landscape lighting application[END_REF][START_REF] Nakano | Application of multispectral camera to color rendering simulator[END_REF][START_REF] Sándor | Visual color rendering based on color difference evaluations Lighting[END_REF]. Moreover, the redgreen-blue LED clusters have been recently shown to render more object colours with increased saturation rather than with high fidelity [START_REF] Žukauskas | Solid-state lamps with optimized color saturation ability[END_REF]. This stimulates a search for new colour quality metrics, which could better comply with the visual ranking and be able to resolve the problem of assessing colour rendition properties of light sources, including those containing narrow-band electroluminescence emissions.

In this paper, we address the problem of colour quality of solid-state light sources in order to validate different metrics and provide guidelines for composing SPDs of single-chip LEDs and LED clusters with different and controllable colour rendition characteristics.

The paper is organized as follows. In section 2, approaches to assessing colour quality of illumination are considered. In section 3, various solid-state lamps, as well as fluorescent lamps, are rated with respect to different colour rendition properties and suggested to categorize into several distinct colour-quality groups. In section 4, a summary of the survey is presented.

Colour quality metrics

In this section, several metrics for assessing colour-rendition quality of light sources are considered and compared. We start with CRI, which has been introduced for ranking fluorescent lamps and persists as a standard metric for years, in spite of numerous proposed improvements and alternatives (see, e.g. Ref. [START_REF] Guo | A review of colour rendering indices and their application to commercial light sources Lighting[END_REF] for a review). Other metrics considered here are the two recent approaches that were developed in order to meet an increasing demand for the improved assessment of LED-based light sources. These two metrics are the colour quality scale (CQS), which is an attempt to develop a more general approach to colour quality basing on the method of colour differences used in CRI, and the statistical approach to colour quality, which is a method radically different from CRI. Since CRI and CQS lack means for ranking colour-saturating sources, these metrics are considered in combination with appropriate gamut-area approaches that mitigate this drawback.

Colour rendering index and gamut area (U*V*W* colour space)

CRI is the most widely used metric for rating light sources in colour rendition. Introduced by the International Commission of Illumination (Commission Internationale de l'Éclairage, CIE) in 1965 (see Ref. 12 for the latest edition), CRI relies on numerically estimating colour differences for particular test colour samples when a reference source is replaced by that under assessment. The colour differences are estimated within the U*V*W* colour space (1964 CIE), which is a nonlinear extension of the u-v "uniform chromaticity scale" colour space (1960 CIE) to three dimensions.

The lightness index W* is related to the luminous tristimulus value and the chromaticness indices U* and V* are derived from the uv chromaticity coordinates and lightness index. The test colour samples are fourteen samples from the Munsell system, which specify colours in hue, chroma and value (lightness). The reference source, which must have the same correlated colour temperature (CCT) as the source under assessment, is either a blackbody illuminant (for CCT below 5000 K) or daylight phase illuminant (for CCT above 5000 K). A small mismatch between the chromaticity of the reference and tested source is allowed and treated using the von Kries chromatic adaptation method. The special colour-rendering indices are derived from the colour shifts ∆E i for each test colour sample,

( ) ( ) ( ) [ ] 2 1 2 2 2 6 . 4 100 6 . 4 100 * * * ∆ + ∆ + ∆ - ≡ ∆ - = W V U E R i i . ( 1
)
The general CRI is the arithmetic mean of eight special CRIs that have moderate chroma (about /6 in average):

= = 8 1 a 1 i i R R . (2)
The general CRI has a maximal value of 100 when the eight colour shifts are almost zero and the scaling parameter 4.6 in equation ( 1) is selected in such a way that R a = 51 for a warm white halophosphate fluorescent lamp. Despite of widely using CRI for ranking light sources and for optimization of SPDs for both conventional [START_REF] Thornton | Luminosity and color-rendering capability of white light[END_REF] and solid-state [START_REF] Žukauskas | Optimization of white polychromatic semiconductor lamps[END_REF][START_REF] Žukauskas | Optimization of white all-semiconductor lamp for solid-state lighting applications[END_REF][START_REF] Ries | Optimized additive mixing of colored light-emitting diode sources[END_REF][START_REF] Ohno | Spectral design considerations for white LED color rendering[END_REF][START_REF] Mirhosseini | Improved color rendering and luminous efficacy in phosphor-converted white light-emitting diodes by use of dual-blue emitting active layers[END_REF] lamps, this metric has numerous drawbacks [START_REF] Guo | A review of colour rendering indices and their application to commercial light sources Lighting[END_REF][START_REF] Van Trigt | Color rendering, a re assessment Color[END_REF][START_REF] Worthey | Color rendering: Asking the question Color[END_REF][START_REF] Cie | Colour rendering of white LED sources Publication[END_REF].

The key feature of CRI is treating colour shifts irrespectively of their direction, i.e. the metric exclusively estimates the ability of a light source to render object colours with high fidelity.

However, subjective perception of various colour distortions is unequal and depends on the direction of the colour shift. For instance, hue distortions are less tolerated than lightness distortions; and distortions that increase saturation are even preferred [START_REF] Hashimoto | Visual clarity and feeling of contrast[END_REF]. Therefore, a unified approach to different directions of the colour shifts is considered as a serious drawback of CRI. In particular, CRI conflicts with subjective visual preferences when a set of sources under ranking includes sources with SPDs containing few narrow-band components [START_REF] Narendran | Color rendering properties of LED light sources Proc[END_REF][START_REF] Shakir | Evaluating white LEDs for outdoor landscape lighting application[END_REF][START_REF] Nakano | Application of multispectral camera to color rendering simulator[END_REF][START_REF] Sándor | Visual color rendering based on color difference evaluations Lighting[END_REF] (as discussed in section 3, such sources can increase or decrease saturation of a considerable number of object colours).

Another CRI drawback is in that the "uniform chromaticity scale" colour space in fact is far from being uniform in respect of perceptually resolved colour differences. In particular, the MacAdam ellipses [START_REF] Macadam | Visual sensitivities to color differences in daylight[END_REF], which are the regions that comprise chromaticities almost undistinguishable to human vision, have very different dimensions in different parts of the u-v chromaticity diagram. Hence, CRI unequally treats distortions of different object colours.

One more drawback of CRI is using a small number of test colour samples. For instance, using 40 test colour samples closely spaced within a "circle" of equal chroma (/6) revealed that CRI misses distortions in many hue directions [START_REF] Stanik Nas | Polychromatic solid-state lamps versus tungsten illuminant: hue changes of Munsell samples[END_REF]. Moreover since vectorial representation of the colour shifts (colour rendition vectors, CRVs) of an enhanced number of test colour samples (~1000) tend to form "clouds" with azimuth (hue) periodicity of colour distortions [START_REF] Van Der | The challenge in communicating color rendition of light sources, The balance between simplicity and accuracy[END_REF], the eight samples of the general CRI can fall into extremes of such periodic distribution yielding large errors in the assessment. A small number of test colour samples used in CRI might be partially related to modest computational resources at the time when the metric was introduced. However, even a more important reason of avoiding a larger number of test colour samples is the arithmetic averaging of special CRIs in the general CRI; such averaging is not suitable for shifts that are very different in magnitude.

The above drawbacks of CRI, as well as some other shortcomings (e.g. limitations of von Kries chromatic adaptation, equal rating of reference sources, and inconvenient scaling that can yield confusing negative values of the indices) poses a problem of the applicability of this metric for the next-generation lighting technology, solid-state lighting, which offers more versatility in the control of colour quality. To that end, CIE conceded that "CRI is generally not applicable to predict the colour rendering rank order of a set of light sources when white LED light sources are involved in this set" and recommended the development of a new colour rendering index [START_REF] Cie | Colour rendering of white LED sources Publication[END_REF].

Despite some pessimism in using CRI, the main drawback of this metric, the disregard of the colour shift directions, can be considerably mitigated by supplementing R a by a figure of merit, which quantifies the ability of light sources to make colours appear "vivid" and easy to distinguish.

Basically, this ability manifests itself by increasing saturation of object colours. Examples of such colour-saturating-related figures of merit are the flattery index [START_REF] Judd | A flattery index for artificial illuminants[END_REF] and the colour-discrimination index [START_REF] Thornton | Color-discrimination index[END_REF]. A similar figure of merit, which pertains to the CRI metric, is the gamut area index (GAI) [START_REF] Rea | Color rendering: A tale of two metrics[END_REF]. GAI is the relative change in the area of the polygon defined by the coordinates of the eight CRI test colour samples in the 1964 CIE U*-V* plane when a reference source is replaced by that under test (see figure 1). GAI employs a single flat-spectrum reference illuminant (CIE illuminant E), which allows comparing sources with various CCT on the absolute scale (sources with lower CCT inherently have lower values of GAI).

Although GAI suffers from many drawbacks peculiar to the general CRI (small number of test colour samples, lack of uniformity of the colour space, etc.), it might be useful for comparing colour rendition characteristics of different sources [START_REF] Rea | Color rendering: A tale of two metrics[END_REF]. However, GAI should be applied with care, since it integrates both positive and negative contributions to gamut variation, i.e. increased saturation of some test colour samples can be compensated by decreased saturation of other samples with a reduced effect on the net gamut area. Figure 1 demonstrates this effect for a daylight pc LED. Here the gamut area under the LED amounts only 85% of that under the reference illuminant, whereas two of the eight test colour samples (3 and 7) gain in saturation.

Colour quality scale and gamut area scale (CIELAB colour space)

CQS is a metric developed at the National Institute of Standards and Technology (NIST) for mitigating the main drawbacks of CRI [START_REF] Ohno | Toward and improved color rendering metric[END_REF], especially the absolute focus on colour fidelity. The metric employs a set of 15 test colour samples that have somewhat larger chroma (about /11 in average) than those used in CRI and an improved colour space (CIELAB) that is much more equidistant in respect of perceivable colour differences than the U*V*W* colour space (figure 2).

One of the main ideas of CQS is to take into account subjective colour saturation preferences by quantifying the ability of a light source to render object colours with high fidelity and the ability to render colours with increased saturation within an integral figure of merit. This is achieved through the introduction of a reduced colour difference, which excludes the increase of saturation. For an ith test colour sample, the reduced colour difference can be presented as

( ) ( ) ( ) 2 1 2 4 2 * Re ∆ + ∆ - + ∆ = ∆ L C H E i , (3)
where ∆H, ∆C, and ∆L are the shifts in hue, chroma, and lightness, respectively, when a reference source is replaced by that under assessment. Bold lines in figure 2 depict the reduced colour shifts with only negative chromatic shifts taken into account (samples 1, 2, 3, 8, 9, 10, 11, and 15) and with positive chromatic shifts excluded (samples 4, 5, 6, 7, 12, 13, and 14).

Another improvement of the CQS metric is using the root-mean-square (RMS) of the reduced colour differences in order to ensure that a large colour difference for any sample has a higher influence on the overall rating:

( ) = ∆ = ∆ 15 1 2 * * RMS 15 1 i i E E . (4)
In order to avoid negative values of the score, a nonlinear conversion to a 0-100 rating scale is used in the CQS metric:

[ ] { } 1 301 . 0 10 exp ln 10 CQS * RM + ∆ - = S E , (5)
where 0.301 is the scaling factor selected such that that the average CQS score for a standard set of fluorescent lamp spectra is equal to the average general CRI for the same set of lamps.

One more improvement of the CQS metric in respect of CRI is the derating of light sources with very low and very high CCTs (below 3500 K and above 6500 K, respectively) in order to take into account the reduced gamut area of the set of the test colour samples. (However, such a derating is ambiguous, since some individuals exhibit the effect of colour constancy that compensates the reduction of the gamut area [START_REF] Zukauskas | Color perception under illumination by quadrichromatic solid-state lamp[END_REF].)

Despite the regard to colour saturation preferences, the CQS metric is unable to completely distinguish between light sources that have different ability in saturating object colours. For instance, a source that renders the colour of a jth sample with increased chroma (∆C j > 0) can have the same CQS score as another source that renders the colour of the same sample without increased (∆C j = 0). Another drawback of CQS is still a relatively low number of test colour samples comparing to the actual number of object colours distinguished by human vision.

The former drawback of the CQS metric can be mitigated in the same way as in the case of CRI, i.e. by the supplementing the CQS score by an appropriate gamut-area-based figure of merit.

By analogy with GAI, which is the supplement to CRI, a relative change in the area of the polygon defined by the coordinates of the 15 CQS test colour samples in the a*-b* plane of the CIELAB colour space can be employed. Such a relative change (designated here as the gamut area scale, GAS) has been already used for the optimization of SPDs of tetrachromatic LED-based light sources [START_REF] Ohno | Spectral design considerations for white LED color rendering[END_REF]. In order to completely match GAS with CQS, derating of the sources with extreme values of CCT can be applied [START_REF] Ohno | Toward and improved color rendering metric[END_REF] instead of using a single reference source as in GAI. It is to be noted that GAS has the same limitations as GAI due to the compensation of positive and negative shifts in chroma of different test colour samples (see figure 2).

Statistical approach to colour rendition

One of the main shortcomings of the CRI metric, a small number of test colour samples, is still present in CQS and is difficult to avoid when an averaging of the colour shifts is used. For a large number of test samples, several alternative approaches can be applied. For instance, a large number of test colour samples can be subjectively sorted into several categories basing on colour names.

The results of sorting for a tested lamp can be compared in respect of a reference illuminant and quantified by appropriate indices corresponding to various colour rendition characteristics. Several metrics of such categorical colour rendering have been proposed [START_REF] Boynton R M | Categorical color rendering of four common light sources[END_REF][START_REF] Yaguchi | A proposal of color rendering index based on categorical color names[END_REF]. Another example of a large-sample-number approach is graphical analysis of a set of CRVs [START_REF] Worthey | Color rendering: Asking the question Color[END_REF][START_REF] Van Der | The challenge in communicating color rendition of light sources, The balance between simplicity and accuracy[END_REF]. An advanced approach is the computational sorting of the CRVs to several groups depending on the type of colour distortion and statistical analysis of the sorting results [START_REF] Žukauskas | Statistical approach to color quality of solid-state lamps[END_REF].

A statistical approach introduced in Ref. [START_REF] Žukauskas | Statistical approach to color quality of solid-state lamps[END_REF] relies on several basic principles. First, it avoids using colour spaces, which in fact are non-ideal analytical approximations of perceptually uniform colour space. Instead, the behaviour of the CRVs is analysed in respect of the colour-discrimination shapes, which are built basing on the experimental data on just perceivable colour and luminance differences estimated individually for each colour test sample. Figure 3 shows such a shape, which is an elliptical cylinder with the cross-section identical to a triple-sized region of the just perceivable chromaticity and the half-height equal to three times the just perceivable luminance difference. The regions of the just perceivable chromaticity are the interpolated MacAdam ellipses [START_REF] Macadam | Visual sensitivities to color differences in daylight[END_REF], which can be presented within any colour space; and the just perceivable luminance difference is 0.7% [START_REF] Wyszecki | Color Science: Concepts and Methods, Quantitative Data and Formulae[END_REF]. The second principle of the statistical approach is in that a CRV is not continuously quantified in magnitude and direction, but discretely scored to a particular colour rendition index depending on its behaviour in respect of the colour-discrimination shape. If the CRV for a test colour sample dos not escape from the shape, the colour is considered as rendered with high fidelity (indistinguishably from the reference source) and the sample is scored to colour-fidelity index (CFI). If the CRV escapes from the shape, the sample is scored to at least one of several statistical colour-distortion indices depending on the projections of the vector that exceed the size of the shape. For instance, when a CRV has an excess projection directed toward increased or decreased chroma, the sample can be scored to the colour saturation index (CSI) or colour dulling index (CDI), respectively. Similarly, a CRV with an excess projection directed toward different hue or along the luminance (vertical) axis can be scored to the hue distortion index (HDI) or luminance distortion index (LDI). (CDI and LDI are introduced here in addition to CFI, CSI, and HDI defined in Ref. [START_REF] Žukauskas | Statistical approach to color quality of solid-state lamps[END_REF]. Each index measured in the percentage of the scored samples quantifies a particular colour rendition characteristic of a light source within the single statistical format. An extended statistical representation of colour rendition characteristics of a light source (e.g. behaviour of the CRVs of particular hues) is a colour quality chart [START_REF] Žukauskas | Statistical approach to color quality of solid-state lamps[END_REF], which displays the CRVs scored to different indices within an appropriate colour space (e.g. CIELAB).

Differently from colour-shift-averaging metrics (CRI and CQS), the magnitudes of the CRVs are not decisive in the statistical approach, once a very large number of test colour samples is employed (a larger value of a colour-distortion index implies a higher possibility of the presence of CRVs with larger respective projections). An appropriate set of test colour samples is the spectrophotometrically calibrated palette of 1269 Munsell samples [START_REF]Spectral Database[END_REF].

It should be noted that the statistical metric exploits MacAdam ellipses, which have been originally defined for a constant luminance (~48 cd/m 2 ) [START_REF] Macadam | Visual sensitivities to color differences in daylight[END_REF]; therefore this luminance value is assigned to all test colour samples irrespectively of their colour lightness. Further development of the method is required in order to extend the assessment of colour distortions for test colour samples having particular lightness under conditions of different luminance. (It is to be noted that CRI and CQS, which use lightness scales, have an opposite drawback in that luminance, which is important in colour discrimination, is not specified and taken into consideration). Also, subjective validation of the statistical method needs developing new approaches because of a very large number of test colour samples used. Finally, the statistical approach requires solving some general problems of colour rendition such as the problems of chromatic adaptation, colour constancy, reference sources, and colour appearance of the samples with different backgrounds taken into account.

Solid-state lamps with different colour rendition properties

Different metrics described in the previous section can be used for assessing colour rendition properties of light sources. Irrespectively of a metric used, the two basic colour quality characteristics of lighting, the ability to render surface colours with high fidelity and the ability to saturate (desaturate) colours, are probably the most important ones for giving subjective preferences of illumination and for rating light sources in colour rendition quality.

In this section, various solid-state sources of light, as well as their ancestors, fluorescent lamps, are considered. The sources are rated using the three above approaches, the general CRI in combination with the relative gamut area for eight standard test samples in the V*U*W* colour space (GAI), CQS in combination with the relative gamut area for 15 test colour samples in the CIELAB colour space (GAS), and the statistical approach, which rely on McAdams ellipses rather than on a colour space and employs 1269 test colour samples.

The lamps under consideration are attributed to three conditional groups of, namely, highfidelity, colour-saturating, and colour-dulling lamps, respectively. Within each group, we compare lamps in terms of colour-fidelity indices (R a , CQS, and CFI), colour-saturation indices (GAI, GAS, CSI, and CDI), as well as two additional statistical indices for hue and luminance distortions (HDI and LDI, respectively).

Here, versatility of solid-state lighting technology in the control of colour rendition properties is demonstrated by simulating SPDs of multiwavelength clusters that are composed of standard coloured and white LEDs. As a model set of commercial LEDs, the Philips Lumileds Lighting Luxeon ® Rebel LED family of 10 typical LEDs [START_REF] Rebel | [END_REF] that meet the needs of display, signage, and lighting industry was employed. This family comprise direct-emission royal-blue (452 nm peak wavelength), blue (469 nm), cyan (512 nm), and green (523 nm) InGaN LEDs; direct-emission amber (591 nm), red-orange (625 nm), and red (637 nm) AlGaInP LEDs; and InGaN-based pc amber (589-nm), daylight and warm white LEDs. The SPDs of the LEDs used in the simulation of multiwavelength lamps were measured at a forward current of 350 mA and at a temperature of the metal pad of 25°C.

High-fidelity lamps

We define high-fidelity light sources as those rendering more than half object colours The colour-saturating ability of these lamps is low and the gamut-area indices are very similar (GAS is around 100% and GAI is around 60% and 100% for CCT of 3000 K and 6500 K, respectively).

Among conventional light sources, this family is contributed by fluorescent multiband lamps, which convert UV radiation to visible light with a rich spectrum provided by a set of wide-band and narrow-band phosphors [START_REF]Lamps and Lighting[END_REF]. Typically, such lamps have CFI of about 70%, and the statistical colour-distortion indices have low values (mostly below 10%).

Fluorescent triphosphor lamps have SPDs that are composed of narrow-band phosphor emissions due to rare-earths ions [START_REF] Žukauskas | Statistical approach to color quality of solid-state lamps[END_REF][START_REF] Žukauskas | Rendering a color palette by light-emitting diodes[END_REF] and therefore are deficient in some spectral components. [START_REF] Žukauskas | Rendering a color palette by light-emitting diodes[END_REF][START_REF] Žukauskas | Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering[END_REF]. However when the objective function is a figure of merit based on a small number of test colour samples, the model SPDs are subjected to a significant variation of the peak positions. For instance, the pentachromatic set of 30-nm components that is optimized in respect of R a have noticeably shorter peak wavelengths of 444 nm, 487 nm, 530 nm, 572 nm, and 622 nm, respectively, [START_REF] Žukauskas | Rendering a color palette by light-emitting diodes[END_REF] and CFI reduced to 96%. This demonstrates that maximizing R a can result in minimizing already undistinguishable chromaticity shifts within the MacAdam ellipses for the eight standard samples and in a loss of fidelity of colour rendition for a larger number of other samples (about 50 in this case). Same applies to CQS, which employs only 15 test colour samples.

Of commercial single-chip LEDs, warm white pc LED, which is an InGaN-based LED with partial conversion of blue electroluminescence in two phosphors (yellow and red), can be attributed to high-fidelity light sources (CFI = 61%). This LED almost does not render object colours with increased saturation and has a modest LDI. The main drawback of this light source is a rather high portion of dulled colours (CDI = 25%). The overall rating of colour quality of the warm white pc LED is in between multiband and triphosphor fluorescent lamps.

Practical solid-state lamps with improved colour fidelity can be realized by assembling commercial direct-emission and phosphor converted LEDs to multiwavelength clusters. Figure 4(a) shows examples of SPDs for tetrachromatic RAGB clusters composed of standard coloured LEDs.

The selection of the LEDs and adjusting their relative partial fluxes was carried out through the solution of an optimization problem with CFI used as an objective function. Within the family of commercial LEDs employed, the highest values of CFI were attained for a tetrachromatic set of red 637-nm, pc amber 589-nm, green 523-nm, and blue 452-nm LEDs (RpcAGB cluster). Of 1269 test colour samples, high fidelity of colour rendition was obtained for 88% and 77% samples for CCT of 3000 K and 6500 K, respectively. Meanwhile, all statistical colour-distortion indices (CSI, CDI, HDI, and LDI) dropped to marginal values. It is to be noted that optimization of practical highfidelity clusters in respect of R a or CQS usually results in the selection of the same set of LEDs, since the choice of peak wavelengths is small. For instance, the above tetrachromatic set optimized in respect of R a (CCT = 3000 K) has partial fluxes of the narrow-band components that differ by less than 10% from those for maximized CFI and the value of CFI is reduced by only 1%.

High CFIs are also available for clusters, where coloured LEDs complement white phosphorconverted LEDs thus mitigating deficiency in some spectral components [START_REF] Vitta | White complementary solid-state lamp[END_REF]. In order to preserve the chromaticity of the lamp on the daylight or blackbody locus, at least two coloured LEDs are to be employed. Figure 4(b) shows SPDs of complementary light sources composed of a warm white LED and two coloured LEDs. Colour-fidelity characteristics of such sources (table 1) are considerably higher than those of the solitary warm white LED and are similar to those of tetrachromatic clusters that comprise a pc amber LED. Typically, values of CFI in excess of 80% can be attained.

Even higher colour-fidelity of illumination can be provided by complementary lamps composed of a warm white LED and three coloured LEDs (figure 4(c)). These lamps have CFI well above 90%. Similar extreme colour-fidelity characteristics are obtained for a pentachromatic cluster composed of coloured LEDs (figure 4(d)). The latter cluster differs from the above tetrachromatic one in that the second blue LED (469-nm) is added (RpcAGBB cluster).

Colour-saturating lamps

Colour-saturating lamps can be defined as those rendering colours of the major portion of a high number of test colour samples with increased saturation (CSI > 50%). Such lamps can find applications that require improved colour discrimination and/or increased colourfulness, e.g. in some work environments, as well as in commercial, entertainment, and architectural lighting.

Colour-saturating lighting is subjectively preferred in respect of high-fidelity lighting in short-term visual experiments, although it is a question whether colour-saturating preferences persisted in general lighting, which implies long-run visual convenience. The SPDs of colour-saturating lamps basically differ from those of high-fidelity lamps in that the spectrum is void of the component in the 530-610 nm wavelength range.

Colour rendition indices of colour-saturating lamps are presented in table 2. Basically, such lamps have reduced colour-fidelity indices and a very low CDI and noticeably distort hue and luminance of surfaces. This category of lamps is peculiar in that their CQS score is larger than R a due to the intentional disregard of colour-saturating effect in the CQS metric. Also, one can notice that the colour saturating effect can be higher at lower CCTs.

Conventional colour-saturating light source is a neodymium-glass filtered incandescent lamp, which is known for years [START_REF] Bouma | The colour reproduction of incandescent lamps and 'Philiphan' glass Philips[END_REF]. Such lamp renders about 52% of 1269-element Munsell palette with increased saturation, while still a considerable portion of test colour samples (37%) are rendered with high fidelity and HDI and LDI have moderate values. It is to be noted that gamut-area indices (GAI and GAS) of the lamp do not substantially differ from those of high-fidelity lamps with low CCT. This indicates on the insensitivity of these indices to colour-saturating properties of some light sources.

Another example is a colour-saturating source comprising three narrow-band red, green, and blue emitters [START_REF] Thornton | Fluorescent lamps with high color-discrimination capability[END_REF][START_REF] Mccann | Quantitative studies in retinex theory: A comparison between theoretical predictions and observer responses to the 'Color Mondrian' experiments[END_REF], for instance a lamp known from experiments on visual perception, which contains 10-nm wide components with the spectral peaks at 630, 530, and 450 nm, respectively [START_REF] Mccann | Quantitative studies in retinex theory: A comparison between theoretical predictions and observer responses to the 'Color Mondrian' experiments[END_REF]. This RGB lamp has CSI in the range of 70% to 80% depending on CCT and huge gamut-area indices. However many test colour samples, especially those with increased saturation, experience hue and luminance distortions (typically HDI and LDI are around 70%) and colours of very few samples (< 10%) are rendered with high fidelity. High colour saturating effect can be also attained for a dichromatic blend of narrow-band red and green emitters (not shown in table 2). However, such an RG lamp has even higher HDI (actually, no other hues except red and green are rendered).

Design rules for colour-saturating solid-state lamps were considered in Ref. 17. Such lamps are direct-emission-LED RGB clusters that do not cover the spectral region between 530 nm and 610 nm. Provided that this spectral gap is kept unimpaired, the colour-saturating ability of the clusters is rather insensitive to the peak positions of the LEDs. Several triads of commercial coloured LEDs can be employed, for instance, a 637-512-469-nm RCB cluster or a 637-523-452-nm RGB cluster (see table 2 and figure 5). Such clusters can have CSI around 70% and higher, low CFI and high values of HDI and LDI, similarly to the narrow-band RGB emitter.

Because of the absence of the 530-610-nm component, colour-saturating LED clusters have reduced LER in comparison with other lamps. Again, since the choice of the peak wavelengths of commercial LEDs is small, maximization of any of the three colour-saturation indices (CSI, GAI or GAS) can be used for the selection of the RGB components with very similar result.

Colour-dulling lamps

Some light sources have CDI in excess of 50% and therefore can be designated as colour-dulling lamps. The general CRI of these lamps is below 80 and currently they are only used in general lighting applications where no regard to colour quality is paid. (However, a potential for using them in specific applications, were desaturated colours might be preferred, e.g. for colour vision relaxation or for some medical or cultural environments, still needs unveiling.) The SPDs of such lamps must have a component in the 530-610 nm range, which is absent in colour-saturating lamps.

However differently from high-and medium-fidelity lamps, they usually lack the component in the wavelength range beyond 610 nm and in some cases rely only on a dichromatic yellow-blue (YB) system [START_REF] Worthey | Color rendering: Asking the question Color[END_REF].

Colour rendition indices of colour-dulling lamps are presented in table 3. The lamps are seen to render a modest portion of object colours with high fidelity (CFI <30%) and have R a and CQS score very similar to those of colour-saturating lamps (however, none of these two indices has advantage over another one as in the case of colour-saturating lamps). Almost no object colours gain in chroma (CSI is close to zero) and HDI and LDI of practical colour-dulling lamps are somewhat smaller than those of colour-saturating counterparts. Also, higher values of CDI are attained at lower CCT.

Conventional colour dulling lamps are dichromatic halophosphate fluorescent lamps. They have CDI of 50% to 70%.

Table 3 also displays data for colour-dulling YB lamps composed of 30-nm wide emitters, which have extremely high CDI, as well as HDI and LDI (no hues other than blue and yellow are rendered [START_REF] Worthey | Color rendering: Asking the question Color[END_REF]). With increasing bandwidth, the modelled YB lamps exhibit a decrease in all colourdistorting statistical indices and an increase in fidelity indices. The colour-dulling effect persists (CDI > 50%) for the band widths of the components up to 100 nm.

Of practical solid-state light sources, a typical colour-dulling lamp is the two-component daylight white LED with partial conversion of blue light emitted by the InGaN chip to yellow light emitted by cerium-doped yttrium-aluminium-garnet (YAG) phosphor. This LED has CDI of 53% and also makes many test colour samples appear as having distorted hue and luminance.

Colour-dulling lamps can also be composed of practical coloured LEDs. The highest values of CDI are obtained for trichromatic LED clusters containing direct-emission amber, green, and blue

LEDs. Figure 6 shows examples of SPDs for the trichromatic AGB clusters containing standard coloured LEDs (amber 591-nm, green 523-nm, and blue 452-nm). These clusters have CDI of 51% and 67% for CCT of 3000 K and 6500 K, respectively. It should be noted that the AGB clusters have the largest LER of all solid-state lamps due to the absence of the component in the spectral range beyond 610 nm.

Discussion and conclusions

In the following we discuss and summarize the above analysis of different colour quality metrics and assessment of colour rendition properties of various solid-state lamps.

High values of R a and CQS score (≥90) indicate on high colour fidelity of a lamp. However these two figures of merit, which actually measure either only colour fidelity (CRI) or evaluate colour fidelity with regard to colour-saturating preferences (CQS), fail to distinguish between lamps that have different colour-saturating properties (except when used both, the condition CQS > R a indirectly indicates on the colour-saturating ability). This is the reason for that the CRI and CQS metrics, which average colour rendition data for a relatively small number of test colour samples, have limited applicability in solid-state lighting technology, which exploits narrow-band components not only in high-fidelity lamps, but also in colour-saturating lamps, such as RGB LED clusters. This drawback can be mitigated by supplementing the CRI and CQS metrics by gamut-area indices, such as GAI or GAS, respectively. However because of a poor overlap of the narrow-band components of the solid-state lamps with the reflection spectra of a small number of test colour samples involved and compensation of the positive and negative contributions to saturation within the gamut area, in some cases these gamut-area indices are rather insensitive and even miss the coloursaturating effect. Also GAI, which is based on a single reference illuminant, is somewhat inconvenient in that it always has values below 100 for low-CCT lamps, even for those exhibiting a high colour-saturating effect in respect of a blackbody radiator. LED clusters offer more versatility in colour rendition engineering. RGB and AGB clusters composed of narrow-band direct-emission LEDs are the lamps with high colour-saturating and colour-dulling ability, respectively. Since the narrow-band RAGB LED cluster has rather high colour-fidelity indices [START_REF] Stanik Nas | Polychromatic solid-state lamps versus tungsten illuminant: hue changes of Munsell samples[END_REF][START_REF] Žukauskas | Statistical approach to color quality of solid-state lamps[END_REF], colour quality of such a cluster can be traded off between all three colour-rendition properties (fidelity, saturating, and dulling) by the variation of the partial fluxes of the coloured LEDs.

LED clusters with extreme colour-fidelity indices require covering the entire spectrum. In particular, a broad-band 530-610-nm component that prevents from colour saturating and a component in the wavelength range beyond 610 nm that that prevents from colour dulling are required. Such clusters can be implemented in several ways by ether complementing white pc LEDs by two or three direct-emission coloured LEDs or by using a multichip approach based on at least four coloured LEDs. In the latter case, broad-band pc coloured LEDs, such as pc amber LED, are preferred in order to reduce the number of components. An example of such a lamp is the RpcAGB cluster. Provided that the driving circuitry of this cluster allows extinguishing the amber LED and adjusting the partial fluxes of the rest (RGB) LEDs, illumination with dynamically traded off colour fidelity and colour saturating can be realized. The development and subjective assessment of such clusters with a dynamical trade-off between different colour rendition characteristics is a subject of our future work.

Figure 1

 1 Figure 1 illustrates the use of the CRI metric. The circles in the U*V* plane of the 1964 CIE

  indistinguishably from reference sources (CFI > 50%) and having low values of statistical indices that signify increased of decreased saturation and distortions of hue and luminance (CSI CDI, HDI, and LDI, respectively). Such lamps are able of mimicking sunlight (for high CCTs) or incandescent (halogen) lamps (for low CCTs) and can be used for illuminating scenes that require extreme naturalness of colours. The SPDs of high-fidelity lamps have multiple narrow-band components that tightly cover the visible spectrum. Because of a large number of components needed, selection of the components and finding the partial fluxes of those require solving problems of additive colour mixing through optimization of target functions within multiparametric spaces[START_REF] Žukauskas | Optimization of white polychromatic semiconductor lamps[END_REF][START_REF] Žukauskas | Optimization of white all-semiconductor lamp for solid-state lighting applications[END_REF][START_REF] Mirhosseini | Improved color rendering and luminous efficacy in phosphor-converted white light-emitting diodes by use of dual-blue emitting active layers[END_REF].Colour rendition indices of high-fidelity lamps are presented in table 1. Light sources with CFI > 50% are seen to typically have R a in excess of 90 and CQS scores smaller by several points.

Figure 1 .

 1 Figure 1. Colour coordinates of the eight colour test samples used in the CRI metric in the U*-V*

Figure 2 .

 2 Figure 2. Colour coordinates of the 15 colour test samples used in the CQS metric in the a*-b*

Figure 3 .

 3 Figure 3. Colour discrimination shape (elliptical cylinder) used in the statistical approach to the

Figure 4 .

 4 Figure 4. Spectral power distributions of high-fidelity multiwavelength solid-state lamps for correlated

Figure 5 .

 5 Figure 5. Spectral power distributions of colour-saturating multiwavelength solid-state lamps for correlated

Figure 6 .

 6 Figure 6. Spectral power distributions of colour-dulling amber-green-blue LED clusters for correlated

Table 1 .Figure 1 .Figure 2 .Figure 3 .Figure 4 .

 11234 Figure 1. A. Žukauskas et al. Colour rendition …

  To that end, statistical approach, which is based on sorting a large number of test colour samples, offers a radically improved assessment of colour quality of lighting. Although our analysis of various light sources involved a rather large number of statistical indices (five), the statistical metric can identify the principle colour rendition properties of lamps basing on only two of them, CFI and CSI. High fidelity lamps have high CFI and low CSI; colour-saturating lamps have low CFI and high CSI; and colour-dulling lamps have both CFI and CSI low. It also important that differently from the supplementary CRI/GAI and CQS/GAS metrics, the statistical approach

	measures different colour rendition characteristics within a single format, the percentage of test
	colour samples rendered in different way. This makes the statistical metric convenient not only in
	communication to the end user, but also in trading off different colour rendition characteristics
	within a single solid-state lamp, such a "smart" LED cluster with the individual control of the
	coloured fluxes.
	Colour rendition characteristics of conventional white pc LEDs depend on the number of
	phosphors used. Dichromatic InGaN:YAG:Ce 3+ daylight LED actually is a colour-dulling lamp,
	which can find only limited applications in general lighting. Warm white trichromatic LED with
	partial conversion already renders the major portion (~60%) of object colours with high fidelity.
	Meanwhile, one can anticipate that pc LEDs with complete conversion within a triphosphor blend

can compete in extreme colour fidelity with multiband fluorescent lamps.

Acknowledgments

The work at RPI was partially supported by the National Science Foundation (NSF) Smart Lighting Engineering Research Center (# EEC-0812056).


I Babu
email: i.babu@tue.nl

D A Van Den Ende

G De With

Processing and characterization of piezoelectric 0-3 PZT/LCT/PA composites

PZT/LCT/PA (Lead Zirconate Titanate Pb(Zr 1-x Ti x )O 3 /Liquid crystalline thermosets/Polyamide) composites of 0-3 connectivity were fabricated by hot-pressing. Commercially available PZT powder was calcined at different temperatures for the optimization of the composite properties. The phase transition during calcination of the powder was studied by X-ray diffraction and the particle size by light scattering and scanning electron microscopy. The relative permittivity r , piezoelectric charge constant d 33 , conductivity σ and elastic modulus E of the composites were found to increase with increasing ceramic volume fraction . The obtained d 33 and g 33 values of this newly developed PZT/LCT/PA composite with 50 volume percent PZT using a low poling voltage of 60 kV/cm and poling time of 30 minutes are 42 pC/N and 65 mVm/N, respectively, which are high values for this volume fraction in comparison with the other 0-3 composites reported. Good agreement was found between the experimental data of relative permittivity and piezoelectric constants with several theoretical models (Jayasundere, Yamada and Lichtenecker) of 0-3 composites. In order to assess the correlation of the experimental data with the theoretical models, the experimental data obtained from PZT/PA composites were also included.

Introduction

Sensors and actuators based on piezoelectric ceramic-polymer composites, so-called smart materials, offer a high potential for high tech systems. These composite materials provide superior overall performance over conventional pure ceramics in having good elastic compliance while maintaining good durability. Usually they are optimized for special applications and the demand for these materials has led to extensive research during the past three decades [1][2][3][4]. One of the most used piezoceramics in these types of composites is lead zirconate titanate Pb(Zr 1-x Ti x )O 3 (PZT) which is a typical piezoelectric material having the perovskite crystal structure. PZT shows excellent electromechanical piezoelectric properties at the morphotropic phase boundary due to the coexistence of the tetragonal and rhombohedral phases and its properties are influenced by the variation in composition [START_REF] Jaffe | Piezoelectric ceramics[END_REF].

The types and number of phases, composition, and connectivity of the individual phases determine the properties of the composites. Newnham et al. [START_REF] Newnham | [END_REF] introduced the concept of 0-3 connectivity (a three dimensionally-connected polymer matrix filled with ceramic particles) for the classification of composites. Polymer composites with 0-3 connectivity have several advantages over other types of composites: their ease of production, their ability for the properties to be tailored by varying the volume fraction of the ceramic inclusions and the ease of obtaining different sizes and shapes.

Recently, a number of articles were published on 0-3 composites showing an increased demand on this type of composites [7][8][9][10]. The recently developed PZT/ liquid crystalline thermosets (LCT) [11] composites by van den Ende et al. [12] showed excellent high temperature stability. However, although these composites are more flexible than PZT ceramics, they are rather brittle, limiting their potential applications. To overcome this limitation and be able to realize fairly flexible composites with high permittivity and piezoelectric charge constant, we developed a new series of 0-3 piezoelectric composites (PZT/LCT/PA) by incorporating PZT5A4 into a matrix of LCT and polyamide (PA11).

In this paper we report on the processing and characterization of these new 0-3 piezoelectric composites.

Hot-pressing was utilized for the fabrication and the effect of the volume fraction of PZT on the composite properties was studied. For comparison also PZT/PA composites were studied. A comparison of the experimental results for relative permittivity r , piezoelectric charge constant d 33 , piezoelectric voltage coefficient g 33 obtained for these composites with several theoretical models were made.

Experimental

Materials

The PZT powder used in this research is a half-product of the commercial PZT ceramic PZT5A4 (Morgan Electro Ceramics, Ruabon UK), a soft PZT with 1 mol% Nb added as dopant. The LCT polymer used are phenylethynyl end-capped oligomers based on 6-hydroxy-2-naphthoic acid (HNA) and 4-hydroxybenzoic acid (HBA) (M n = 9000 g mol -1 , HBA/HNA ratio of 73/27), obtained from TU Delft. The amide was PA11, obtained from Aldrich Chemical Company (T g = 46 °C, T m = 198 °C). The PZT powder was calcined at different temperatures (Table 1) with a heating rate of 3 °C /min and a 60 minute hold at the required temperature and cooling to room temperature with a temperature ramp of 3 °C /min. Per calcination temperature 20 gram PZT powder was used in an alumina crucible covered with an alumina lid.

Fabrication of composites

Two types of composites were fabricated. PZT/PA composites were made in order to optimize the calcination temperature and to correlate the theoretical results with PZT/LCT/PA composites.

PZT/LCT/PA composites were made with the optimized PZT. Temperatures in the range of 800 to 1300 °C were utilized for optimization.

In order to optimize the calcination temperature, PZT/PA composites were fabricated with 40 volume percent calcined PZT at different temperatures and 60 volume percent PA11. For the correlation of the results with PZT/LCT/PA composites, PZT/PA composites were fabricated with five different volume percent of PZT. The raw materials were initially mixed by hand with a spatula at room temperature and further ball milled for 60 minutes at 800 rpm. Composites with specific dimensions of 14 mm in diameter and 280-300 µm thickness were fabricated by hot-pressing with an applied force of 90 kN. Fig. 1 shows the various PZT/LCT/PA composites fabricated. The corresponding volume percent of PZT and LCT were premixed in an aluminum boat by hand with spatula. This aluminum boat was placed on a hot plate at 285 °C and thoroughly mixed with a glass rod until all the LCT was molten. After reaching room temperature, the PA powder was added and mixed well. The above mixture was powdered with a pestle and mortar and thereafter subjected to ball-milling for 60 minutes at 800 rpm. Composites with specific dimensions of 14 mm in diameter and 300-375 µm thickness were fabricated by hot-pressing with an applied force of 90 kN.

The LCT was allowed to melt at 280 °C for 30 min and after that the temperature was increased to 320 °C and kept at that temperature for 30 min for curing the LCT. Circular gold electrodes of thickness 300 nm and an area of 7.85x10 -5 m 2 are sputtered on both sides of the composites using an Edwards sputter coater (model S150B). The poling of the electroded sample is performed by applying an electric field of 60 kV/cm with a Heinziger 10 kV high voltage generator for 30 min at 100 °C (PZT/PA) and 120 °C (PZT/LCT/PA) in a silicone oil bath to ensure uniform heating. The electric field was kept on while cooling to room temperature.

Measurements

The phase identification was done at room temperature with an X-ray diffractometer (Rigaku) with CuK radiation of wavelength 0.15418 nm. The diffraction spectra were recorded in the 2 range of 10-80°with a step size of 0.01°and a scanning speed of 0.4°/minute. The microstructure of the calcined PZT powder and the composites were examined by SEM (FEI, Quanta 3D FEG). The particle size of the calcined powders was determined by light scattering (Beckman Coulter LS230) and also by SEM. The aspect ratio of the particles was estimated by Image J software [15] on the SEM pictures of the calcined and milled powder.

In order to calculate the ac conductivity σ, relative permittivity ε r and the loss tangent tan δ of the composites, impedance data were collected by an impedance analyzer (EG&G Princeton Applied

Research, Model 1025) coupled with a potentiostat (Potentiostat/Galvanostat, Model 283) at room temperature in a frequency range of 50 Hz -5 MHz. The dc conductivity (

g 33 = d 33 / o r (1)
where d 33 is the piezoelectric charge constant in pC/N, o is the permittivity of free space (8.85x10 -12 F/m) and r is the relative permittivity of the composite (for this case taken at 110 Hz). The elastic moduli of the composites were tested in three-point bending in static mode on a TA Instruments Q800 series DMA at room temperature. The dimensions of the specimens tested were 20 mm x 10 mm x 2 mm and for each composition two specimens were measured.

Theory

Various theoretical models have been proposed for the permittivity and piezoelectric properties of the 0-3 composites. Some of the mostly used analytic expressions are briefly discussed here. For a brief review we refer to [20] while [START_REF] Sihvola | Electromagnetic mixing formulas and applications[END_REF] provides an extensive discussion.

One of the first, if not the first, model for understanding the dielectric behavior of composites, still widely used, was given in 1904 by Maxwell Garnett [START_REF] Sihvola | Electromagnetic mixing formulas and applications[END_REF]. In his model spherical inclusions are embedded in a polymer matrix without any kind of interaction resulting in

= p {1+[ 3 c ( c -p / c + 2 c )] / [1 -c ( c -p / c + 2 c )]} ( 2
)
where c is the volume fraction of the inclusions and , c and p are the relative permittivity of the composite, ceramic particles and matrix, respectively. Lichtenecker provided in 1923 a rule of mixtures, also still widely used, that reads

c c 1 p c ϕ ϕ ε ε ε - = (3)
Although initially largely empirical, in 1998 Zakri et al. [26] provided a theoretical underpinning of this rule.

In 1982 Yamada et al. [18] proposed a model to explain the behavior of the permittivity, piezoelectric constant and elastic constant of a composite in which ellipsoidal particles are dispersed in a continuous medium aligned along the electric field. Their model shows excellent agreement with experimental data of PVDF-PZT composites. Their final equations read

- - + - + = ) 1 )( ( ) ( 1 c p c p p c c p ϕ ε ε ε ε ε ϕ ε ε n n (4) c c p Gd d ϕ α = and ( 5
) ) 1 3( 1 with ) 1 )( ( ) ( 1 p p c p c p p c c p ν ν ϕ ϕ - + = - - + - + = n' E E n' E E E E E (6)
where n = 4 /m is the parameter attributed to the shape of the ellipsoidal particles, c is the volume fraction of the inclusions and , c and p are the relative permittivity of the composite, ceramic and the matrix, respectively. Further, is the poling ratio, G = nε / [nε + (ε c -ε)] is the local field coefficient and d c is the piezoelectric constant of the piezoceramic while d is the piezoelectric constant of the composite.

Finally the elastic modulus E contains, apart from the above mentioned quantities, a factor n′ directly calculated from Poisson's ratio ν p of the matrix. The condition that the particles are considered to be oriented ellipsoids might seem to be a significant restriction but it has been shown [26] that composites with an arbitrary distribution of ellipsoids with respect to the electric field direction can be transformed in to an equivalent composite with ellipsoids aligned along the electric field direction but with different aspect ratio's for the ellipsoids. This largely removes the restriction mentioned, although the interpretation in micro structural terms becomes more complex. Since their model also provides an expression for the elastic modulus, we have chosen this model mainly to analyze our experimental results.

Another model relatively simple model for the permittivity was provided by Jayasundere et al. [21]. The

final expression reading ) 2 )/( ( 3 )[1 2 ( 3 )] 2 )/( ( 3 )][1 2 /( [3 p c p c p p c p c p p c p c c p c p c c p p ε ε ε ε ϕ ε ε ε ϕ ϕ ε ε ε ε ϕ ε ε ε ϕ ε ϕ ε ε + - + + + + - + + + = / (7)
is a modification of the expression for a composite dielectric constant of a sphere with permittivity ε c in a matrix with permittivity ε p by including interactions between neighboring spheres. The comparison with experimental data appeared to be excellent. Hence this model was applied as well.

Many other models resulting in analytical expressions have been proposed. We mention here only the models by Furukawa et al. [19], Bruggeman et al. [8], Maxwell-Wagner [22], Bhimasankaram et al. [20] and Wong et al. [27]. Most models deal only with part of the full piezoelectric problem and only partially combined solutions were given. E.g. based on the Bruggeman method [29,30], taking permittivity and conductivity into account, or based on the Marutake method [31], taking permittivity piezoelectric coefficients and elastic compliance into account. The latter already requires numerical solution. Recently complete numerical solutions to the fully coupled piezoelectric equations for ellipsoidal inclusions of the same orientation have been provided [28] predicting giant piezoelectric and dielectric enhancement. No experimental evidence for this effect was presented though while a significant conductivity is required rendering the options for practical applications probably less useful.

Results and discussion

Optimization of PZT

X-ray diffraction

The XRD patterns of PZT5A4 powder before and after calcination at different temperatures (800 to 1300 °C) are shown in figure 2. The X-ray diffraction pattern of the PZT5A4 before calcination shows the coexistence of both rhombohedral (200)R and tetragonal phases [(002)T, (200)T] together with the presence of a pyrochlore phase. Calcination resulted in the disappearance of the rhombohedral perovskite structure and in the formation of peak splitting, indicating an increase of tetragonal distortion. The phenomenon of peak splitting and peaks shifting to higher angle with increasing calcination temperature was also reported in previous studies [13,14].

As the calcination temperature increases, the intensity of the pyrochlore phase peaks decrease while the intensity of the tetragonal perovskite peaks increase. This indicates the transformation to almost single phase tetragonal PZT. The PZT calcined at 1100 °C shows a maximum intensity of the tetragonal perovskite peaks at (200)T and (211)T which indicates that at this temperature the material has become (XRD) single phase. From 1150 °C onwards, the peak height decreases as a result of lead loss and also the 2:1 ratio becomes more like 1:1. Zhang et al. reported that the shrinkage of the lattice is believed to result from loss of lead that creates some vacancies in the PZT lattice [14]. The optimal calcination temperature was found to be 1100 °C and PZT5A4 calcined at this temperature was used for composite fabrication.

Particle size analysis

The size of the particles was analyzed by both light scattering and by SEM. Table 1 illustrates the influence of different calcination temperatures on the particle size. The particles were also examined by SEM to get an average size of the individual particles. Comparing the particle size obtained from light scattering with SEM images indicates that the particles are agglomerates.

Figure 3 shows the SEM micrographs of the calcined PZT5A4 at different temperatures. From these micrographs it is observed that, as the calcination temperature increases, the grain size gradually increases, which implies that the particles sinter together during the calcination process. The approximate primary particle size in PZT5A4 calcined at 1000 °C is less than 600 nm, at 1100 °C the average size is about 1.0 µm and as the calcination temperature reaches to 1200 °C, the size of the primary particles becomes 2 to 2.5 µm. The number of particles per agglomerate can be estimated as about (d 50 /d SEM ) 3 . For 1100 °C this yields (2.8/1.0) 3 ≅ 22 primary particles which appears to be not an unreasonable number.

Impedance data

For the fabricated PZT/PA composites, the ac conductivityσ, relative permittivity r , loss tangent tan , piezoelectric charge constant d 33 and piezoelectric voltage constant g 33 were determined. Figure 4 (a) and (b) show the dependence ofσ, r and tan as a function of log frequency with increasing calcination temperature for the PZT/PA composites. From figure 4 (a) it is observed that the ac conductivity is the same for all calcination temperatures and equal to the value for the as-received PZT composite. From figure 4 (b) it is observed that the relative permittivity is in the range from 28 to 38 for the PZT calcined at different temperatures ranging from the as-received PZT powder to the one calcined at 1300 °C. The maximum relative permittivity is observed at 1000 °C and 1100 °C. From 1200 °C, a small decrease in r is observed which may be due to the loss of lead from PZT. The tan has a weak dependence on calcination temperature and is about 0.02 to 0.06 neglecting scattered points.

Piezoelectric charge and voltage constant

The dependence of d 33 and g 33 with increasing calcination temperature is shown in figure. 5. It is observed that the composite using PZT calcined at 1100 °C shows the maximum value of d 33 and g 33 . As the calcination temperature increases, a decrease in piezoelectric voltage coefficient is observed. Since r is nearly constant up to 1150 °C and thereafter decreases but slightly, the g 33 behavior mimics the d 33 behavior closely. This may be due to the decrease in lead content, since the piezoelectric effect is highly dependent on the amount of lead in the PZT. From the above results it is clear that the best quality PZT powder is obtained with a calcination temperature of 1100 °C, consistent with the X-ray results on the PZT powder. Since the particles in the composite are tightly packed with limited agglomeration and porosity, a homogeneous particle distribution results, even for a high volume percentage of PZT, as shown by the SEM images (Figure 11). This probably leads to the comparatively high r values of the PZT/LCT/PA composite in comparison with those of other composites reported in literature (Table 3). The tan has a weak dependence on the volume fraction of PZT ranging from 0.01 to 0.06 if the scattered points are not considered.

Fabrication of the PZT/LCT/PA composite with optimized PZT

Impedance data

Piezoelectric charge and voltage constant

The The data used in the various calculations are given in Table 2. b Data measured at 110 Hz.

c Data from [START_REF]Piezoelectric Materials Data Book 1996 Ferroperm[END_REF]. [17] 120 50 47 PVDF/0.67 PZT [18] 152 48 36 PVDF/0.5 PZT (Hot-press) [9] 95 14 16 PVDF/0.5 PZT (Solution cast) [9] 30 9 36 a 1.5% carbon black added to the PZT-epoxy mixture.

Comparison with theoretical models

In figures 8-10 the experimental data of the PZT/LCT/PA and PZT/PA composites is compared to several models for 0-3 composites, both for dielectric and piezoelectric constants. It is observed that both the composites follow the same trend. In the PZT/LCT/PA, the relative permittivity of the matrix phase was taken to be the combined relative permittivity of the LCT and PA11 phases and was calculated by Lichtenecker's rule of mixtures [23] given by equation 3. The relative permittivity's of virgin LCT and PA11 materials were found to be 3.6 and 3.9, respectively, and the relative permittivity of the ceramic phase was taken to r = 1820 (data Morgan electroceramics, UK). The relative permittivity of the PZT/LCT/PA composite was calculated using Lichtenecker's formula and 2 models for high filler content 0-3 composites, namely Yamada's model [18] and Jayasundere's model [21]. The fit of the equation to the data points of the composites for both these models is plotted in figure 8.

Both Yamada's and Jayasundere's model underestimate the permittivity of the composites, while

Lichtenecker's mixing rule correlates well with the measured values up to 50 volume percent PZT for the PZT/LCT/PA composites. The dielectric behavior therefore, seems to satisfy the logarithmic mixing rule for the PZT/LCT/PA composites. The discrepancy at 60 volume percent is probably due to the fact that at this volume fraction processing becomes much more difficult.

The strong increase in relative permittivity with the increase in PZT volume fraction indicates good coupling of the PZT phase with the polymer phases up to high volume percentages. In both composites the discrepancy between the experimental data and theoretical models is higher at higher volume fraction.

Two effects probably play a role here. According to theory the dielectric constant increases with increasing ellipticity of the particles [18,[START_REF] Sihvola | Electromagnetic mixing formulas and applications[END_REF][START_REF] Sillars | [END_REF]. Moreover, at higher volume fraction the composites, no more act as 0-3 but as 1-3 composites and this is another reason for the high relative permittivity.

In figure 9 the d 33 values are calculated using Yamada's model [18] for high PZT content composites with the d 33 of the ceramic phase taken to be d 33 = 480 pC/N (data Morgan electroceramics, UK). This model was originally developed for PZT/PVDF composites and tested to a PZT content of 70 volume percent.

Since the predicted values mainly depend on the permittivity of the composite and the volume fraction filler, both composites are represented by the same theoretical line. The model shows good correlation of measured d 33 values up to 30 volume percent PZT for both composites, while at 40 and 50 volume percent some deviations occur. For 60 volume percent the estimated values are lower than expected, and as indicated, this may be due to the increased processing difficulties. It is observed that the presence of LCT results in an increase in r and d 33 values. This may be due to some preferred orientation of the LCT around the PZT particles, leading to increased polarisability. The Yamada model incorporates anisotropy effects of the particles by the parameter n. If n = 3, the particles are spherical while n > 3 reflects elongated particles. The best fit for d 33 is obtained with a shape parameter of n = 8.5, which is similar to the value that Yamada et al. found for their composites. To corroborate this, the aspect ratio for 40 particles was estimated from SEM pictures resulting 1.6 ± 0.2, which corresponds to a value of n = 4.6. This factor is lower than the factor of n = 8.5 obtained from fitting the experimental d 33 data to the model. This possibly can be explained by increasing particleparticle interactions at high filling fraction in the composites. When calculating piezoelectric constants using Yamada's model, this translates to a higher n value, which is explained by the model as a higher aspect ratio of the particles. In reality, simply more particles are directly connected which leads to a more direct electromechanical coupling between the particles themselves. Moreover, Yamada's model assumes that all particles are oriented along the direction of the electric field. While this is obviously not true, it has been shown [16] that a random configuration of ellipsoids can be transformed to an equivalent, completely oriented configuration but with different (effective) aspect ratio's. Hence the aspect ratio as observed microscopically not necessarily agrees with the one determined by dielectric measurements.

The combination of LCT and PA11 increases the poling effectiveness, even at relatively low poling voltages. This is evident when comparing d 33 results for the composite with a LCT/PA matrix (figure 7) to the composite with PA matrix only (figure 5). The 40% PZT composite with an LCT/PA matrix has a d 33 value of 1.7 times the value for composite with a PA11 matrix only. The resulting g 33 values are calculated using equation 1. It can be seen in figure 10 that the values calculated using the Lichtenecker model for the relative permittivity and Yamada's model for d 33 correlate reasonably well with the g 33 values of the PZT/LCT/PA composites, while values calculated with the relative permittivity predictions of both other models overestimate the g 33 as a result of the underestimation in relative permittivity.

SEM Morphology

Figure 11 shows the SEM surface morphology of PZT/LCT/PA composites with 20, 30, 40, 50 and 60 volume percent PZT. From these figures it is observed that all the composites have a relative density near to 100%. Moreover, on the scale of tens of micrometers the composites appear to be homogeneous and have a very similar microstructure. From the 60 volume percent PZT image it also becomes clear that the microstructure is also homogeneous at the micrometer scale. The detailed view of structure of the 60 volume percent PZT composite shows the good adhesion of polymer matrix with the ceramic particles.

From these and similar pictures we conclude that the PZT particles are homogeneously dispersed in the polymer matrix and are well adhering to the polymer matrix.

Mechanical properties by DMA

Figure 12 shows the stress-strain curves of the PZT/LCT/PA and PZT/PA composites including the pure polymer and the ceramic volume fraction up to 40 %. The measurements are done at a strain rate of 0.5 % min -1 at room temperature. The three-point bending mode was utilized for these measurements with a preload force of 0.1 N. The upper limit of the static force of the machine is 18 N and the measurements stops when the force reaches this point. Young's modulus E is calculated from the slope near the origin. From the graphs it can be observed that the resulting strain decreases strongly with increasing volume fraction of PZT leading to increasing Young's modulus. Young's modulus ranges from 1050 -3000 MPa for the PZT/LCT/PA composites and from 850 to 4450 MPa for the PZT/PA composites. The modulus obtained for pure LCT (1.0 GPa) is lower than the value of 3.2 GPa as reported by Knijnenberg et al. [11].

However, since the strain rate in the static mode (as used by us) is about 4 orders of magnitude lower than the one for the dynamic mode (as used by [11]) and the former generally leads to lower Young's modulus values, this difference in measuring modes probably explains the difference in elastic values observed.

The elastic modulus of the composites was also calculated according to Yamada's model (Eq. 6) using E c = 37 GPa and ν p = 0.35. While the agreement for the PZT/LCT/PA composites is fair, the agreement for the PZT/PA composites is less good (figure not shown) and we refrain from further discussion.

Conclusions

A series of new 0-3 PZT/LCT/20%PA composites was successfully fabricated and characterized. X-ray diffraction indicated that for the PZT powder used, calcination at 1100 °C shows the maximum intensity for the single phase tetragonal perovskite peaks. The obtained d 33 and g 33 values from PZT/PA composites are also the highest for the PZT calcined at 1100 °C, supporting the above conclusion. The experimental results from r , d 33 and g 33 indicates that the new composites have high r , and possess high d 33 and g 33 values (50 volume percent PZT) of about 42 pC/N and 65 mVm/N. These results compare favourably and show the highest g 33 value in comparison with other reported data in the literature. The experimental data for r agree quite well with the Lichtenecker model for PZT volume fraction up to 50%, while the Yamada and Jayasundere model underestimate the experimental data. The experimental data for the piezoelectric constants agree well with the Yamada model, suggesting an elongated particle shape and confirmed by independent image analysis. Moreover, the addition of PA11 to PZT/LCT composites leads to a lower elastic modulus providing more flexibility to the materials. From the above observations we conclude that these composites are suitable candidate for both sensors and may even show possibilities for actuators.

Dear Editor, Our article, entitled "Processing and characterization of piezoelectric 0-3 PZT/LCT/PA composites" (Article ID: D/352960/PAP), was submitted to Journal of Physics D: Applied Physics on 3 rd April 2010. The editorial decision and reviewer's comments were returned to us on 4 th May 2010. In view of some extension of the work we asked for a somewhat longer response period, which you kindly granted, the deadline being July 30.

We have addressed the reviewer's comments in detail in the attached addenda (Reply to reviewers). We have also amended the manuscript accordingly. Moreover we have highlighted the changes made in the revised manuscript.

Addendum: Reply to reviewers report 1: Referee 1

First of all, we would like thank the reviewers for their comments and we address the various points raised in detail below.

1. The g coefficient was calculated by dividing d on dielectric permittivity (DP). The authors claim, that it has the highest value in nature. However in the experiment DP was measured at 1000 Hz, but d33 at 110 Hz by d33-meter. It is obvious, that it is impossible to measure these parameters at different frequencies and obtain g in such manner. At 110 Hz the DP will be much greater than the same for 1000 Hz due to the excluded mechanisms of polarization in the present study. So, according to my point of view, g-coefficient is calculated in a wrong way.

• We agree with the reviewer's comment that the parameters r and d 33 should be measured at the same frequencies. Indeed we measured the dielectric permittivity r and d 33 at two different frequencies. As expected (at least by us) measurement of the permittivity at 110 Hz, the frequency used for d 33 , showed no difference as compared to the value at 1000 Hz. In fact in the mean time we have shown that r remains the same over a range of frequencies as shown in figure 6 (b) in the revised version of the manuscript, showing the dependence of permittivity as a function of log frequency. From this figure it is observed that the DP remains the same throughout the frequency range. Hence the conclusion is not changed but the text is adapted accordingly. • We agree with the reviewer's comment saying that results of the paper are incomplete without careful analysis of the elastic properties of obtained composite. The elastic modulus of the composites was tested in a three-point bending mode on a TA Instruments Q800 series DMA at room temperature. The obtained results are shown and discussed in section 3.2.4. Mechanical properties by DMA (revised version). • The reviewer states that the Lichtenecker formalism is not applicable if the ratio between the components is higher than 6-7 but does not back this argument with a reference or argument. One could argue that this manuscript proves that the Lichtenecker formula is suitable for higher ratios. However, there is more proof (see A. . We therefore believe the statement mentioned does not hold. Furthermore, we are puzzled by the argument that a model should be disregarded because it is "old". Yamada's article which describes the model continues to be used (cited 48 times since 2005). We introduced a brief section on theory discussing a few of the most important models used.

The

The authors ought to interpret the results obtained in the frame of percolation theory and creation of the cluster by calcination.

• The data were analysed in the frame of other than percolation models. For discrepancies at higher filling fractions percolation may play indeed a role. However, a clear percolation threshold is not observed experimentally and therefore seems to play a minor role. On the other hand, the creation of clusters (we assume the reviewer means agglomerated PZT particles) during calcination does occur and a few remarks about their presence are made in the (original and revised) manuscript.

5.

The figure 9 contains one theoretical and two experimental curves. For which of them the model was applied?

• We assume that the reviewer means one line and two sets of data points from the d 33 measurements for both composites (PZT/LCT/PA and PZT/PA). They are both compared with the Yamada model but since the contribution of the polymer is small anyhow, the prediction is mainly dependent in the volume fraction. The text has been changed accordingly.

6. All the literature is very old and not up-to-date. It has to be rewritten by new actual references.

• We don't agree with the reviewer's comment saying that all the literature is very old and not up-to-date. In order to correlate the performance behavior (permittivity and piezoelectric properties) of a diphase system like 0-3 composites, the mostly used models were from 1904 onwards. Maxwell Garnett developed the first analytic expression to predict the permittivity of a diphase system and the equation is still widely used. (See, for example, Firmino Mendes S et al., 2009, J. Appl. Phys. A, 96, page 900). As said in the response to point 3, a brief section on theory discussing a few of the most important models is introduced.

7.

The data about the parameters of the used components ought to be in a separate table. I recommend to the authors to add also the conductivity of components.

• We agree with the reviewer that a separate • We agree with the reviewer's comment saying that we didn't sufficiently mention in the paper why/how the newly developed material PZT/LCT/PA overcomes the limitation of brittle property of PZT/LCT. The answer to the question why we mentioned the newly developed material PZT/LCT/PA overcomes the limitation of brittle property of PZT/LCT is because we think that the addition of 20% PA will impart some degree of ductility to the present composite, as the elastic modulus is significantly lower. Here we refer to the response to point 2 of reviewer 1. In the revised version elastic data have been added, although strength measurements are not done so far. 2) Page 8. The authors say that "The maximum relative permittivity measured for the PZT/PA composites with different calcinations temperature is 32 for the PZT calcined at 1100 ⁰C." Figure 4 shows that the maximum relative permittivity occurred at both 1000 ⁰C and 1100 ⁰C. Additionally, Figure 4 also shows that tan is not nearly "constant" in the temperature range of 800 to 1300 ⁰C. What is common range of loss tangent? Please check about the statement in this paragraph.

• We thank the reviewer for the constructive comments. It is true that the maximum relative permittivity occurred at both 1000 °C and 1100 °C in the graph but other reasons are indicated to prefer the data at 1100 ºC above those at 1000 ºC. Considering that Xray diffraction showed that the PZT calcined at 1100 °C shows a maximum intensity of the tetragonal perovskite peaks at (200)T and (211)T, indicating that at this temperature the material has become (XRD) single phase, it is concluded that PZT calcined at 1100 °C is the best choice. Nevertheless, based on permittivity data only, 1000 ºC and 1100 ºC are equally 'good'. The text has been changed accordingly. For tan nearly constant means ranging from 2 to 4%. In order to recheck these data we conducted the impedance measurements at room temperature in a frequency range of 50 Hz -5 MHz and the results are presented in the section 3.1.3. Relative permittivity and loss tangent. In order to prevent the doubling of the results we excluded the previous results. The text has been changed accordingly. • According to reviewer's comment we included a new part (Section 2.4. Theory) to explain the analytic expressions that are mostly used for 0-3 composites and also briefly explained the differences between these models. In this study, we compared the obtained experimental results with Yamada, Jayasundere, and Lichtenecker models both for dielectric and piezoelectric constants to observe the correlation between the experimental values and theoretical models. We use the theoretical models to assess the performance of our new materials. The text is adapted accordingly. • We agree with the reviewer's comment saying that the section 3.2.4. (SEM morphology) is not clear. In this section we would like to show the similarity of the morphology of the 20, 30, 40 and 50 vol% PZT. The larger magnification for 60 vol% PZT is to show homogeneity on the micrometer scale while the detailed view is to show the adhesion of ceramic particles to the polymer matrix in 60 vol% PZT. By presenting this we would like to convey that the quality of the composites depends on the homogeneous distribution of the ceramic particles in the polymer matrix which correlates with its effectiveness for improving the properties of the composites. • So, in order to make it clear, we showed all the figures together and marked the last figure as detailed view of the 60 vol% PZT. The text is changed accordingly.

Figure 1 .

 1 Figure 1. Volume fraction of the PZT/LCT/PA composites fabricated with PZT calcined at 1100 °C.

Figure 2 .

 2 Figure 2. XRD patterns of PZT5A4 at different calcination temperatures.

Figure 3 .

 3 Figure 3. SEM micrographs of the PZT5A4 calcined at different temperatures.

Figure 4 (

 4 Figure 4 (a) and (b). Dependence of σ, r and tan as a function of log frequency with increasing calcination temperature for the PZT/PA composites.

Figure 5 .

 5 Figure 5. The dependence of d 33 and g 33 of the PZT/PA composites on the PZT calcination temperature (lines drawn as guide to the eye).

Figure 6 (

 6 Figure 6 (a) and (b) show the dependence of ac conductivityσ, permittivity r and tan as a function of log frequency with increasing PZT volume fraction for the PZT/LCT/PA composites. From figure 6 (a) it is observed that, as the volume percentage of PZT increases, the conductivity increases. Also an increase in r is observed as the volume percentage of PZT increases, due to the increasing contribution of the PZT.

Figure 6

 6 Figure 6 (a) and (b). Dependence of σ, r and tan as a function of log frequency with increasing PZT volume fraction for the PZT/LCT/PA composites.

  dependence of the d 33 and g 33 values of the PZT/LCT/PA composites with increasing volume fraction of PZT is shown in figure7. The d 33 value of the composite shows a continuous increase with increasing volume fraction of PZT, while the g 33 value shows a maximum at 50 volume percent and then decreases when it reaches 60 volume percent. This decrease of g 33 is due to the behavior of d 33 relative to r . A maximum value for d 33 of 46 C/N is observed for the 60 volume percent PZT while for g 33 a maximum value of 65 mVm/N is obtained, both for the 50 volume percent PZT composite.

Figure 7 .

 7 Figure 7. Dependence of the d 33 and g 33 of the PZT/LCT/PA composites with increasing volume fraction of PZT (lines drawn as a guide to the eye).

Figure 8 .

 8 Figure 8. The relative permittivity values of the PZT/LCT/PA and PZT/PA composites as compared to 3 models for 0-3 composites.

Figure 9 .

 9 Figure 9. The d 33 values of PZT/LCT/PA and PZT/PA composites as compared to Yamada's model for piezoelectric composites.

Figure 10 .

 10 Figure 10. The g 33 values of the PZT/LCT/PA and PZT/PA composites as compared to 3 models.

Figure 11 .

 11 Figure 11. SEM surface morphology of the PZT/LCT/PA composites with 20, 30, 40, 50 and 60 volume percent of PZT. The bright colour represents the PZT and the dark background the polymer.

Figure 12 .

 12 Figure 12. Stress-strain curves of the PZT/LCT/PA and PZT/PA composites at room temperature as measured in three-point bending with DMA.

2 .

 2 The results of the paper are still meaningless without careful analysis of the elastic properties of obtained composite. The usage of very soft components, strong percolation of d by 1100 C, and leakage of the initial components require sufficient mechanical tests before usage in technical devices. I recommend resonance method for measuring elastic compliance or stiffness.

3. Page 11 - 13 .

 1113 The authors mentioned theoretical data and models developed by other researchers. Jayasundere, Yamada, and Lichtenecker models have been used in comparison. It will be better if theoretical equations/formulas of other models are presented in this paper. Alternatively, the authors can also briefly explain the differences of these models. Have the tests perfectly performed to generate accurate results or are the theoretical models more accurate? It looks like that the authors use current experimental results as the standard to judge the performances of theoretical models.

4. Page 14 .

 14 The reviewer is not clear about the usage of Section 3.2.4 in the paper? Have the authors tried to present the difference of PZT/LCT/PA composites with 20, 30, 40, 50, and 60 vol% PZT using SEM morphology? Or intend to say PZT particles of these composites are well attached to polymer matrix? Are there any significant differences between the composites with 20, 30, 40, and 50% PZT and the composite with 60 vol% PZT? Please clarify this point.

Table 2 )

 2 is measured as follows. The electrical current was provided by a source measure unit Keithley 237 while the voltage was measured by an electrometer Keithley 6517A. The piezoelectric charge constant d 33 was measured with a

	d 33 meter (Piezotest, PM300) at a fixed frequency of 110 Hz. The piezoelectric voltage coefficient g 33 was
	calculated according to

Table 1 .

 1 Particle sizes of calcined PZT5A4 as determined by light scattering.

	Calcination Temperature (°C)	d 10 (µm)	d 50 (µm)	d 90 (µm)
	PZT5A4 powder	0.23	1.47	3.4
	800	0.88	1.78	3.74
	900	1.00	1.94	3.98
	1000	1.37	2.39	5.23
	1050	1.25	2.16	4.17
	1100	1.38	2.81	9.08
	1150	1.51	3.56	11.07
	1200	1.31	3.61	21.09
	1300	0.71	3.61	17.39

Table 2 :

 2 Table 3 provides the optimum data of r , d 33 and g 33 obtained for the PZT/LCT/PA and PZT/PA composites and a comparison of different polymer/PZT composites as reported in the literature. The d 33 and g 33 values obtained in the present workfollows the same trend as reported by Yamada et al.[18], Satish et al.[16] and Venkatragavaraj et al.[9]. Data of the various components used for the calculations for the composites.

	Satish et al. reported that the hot-pressing is the most reliable method for the fabrication of 0-3
	composites. Moreover hot-pressed composites are known to posses better piezoelectric properties than
	solution-cast composites [9].
	Type	r	tan δ	d 33 (pC/N)	E (GPa)	dc σ (S/m)
	PZT	1820 a	-	480	37 c	-
	LCT	3.6	0.0025 b	0	1.0	1.22⋅10 -11
	PA11	3.9	< 0.035 b	< 0.5	0.83	3.82⋅10 -11

a Data from Morgan Electroceramics.

Table 3 :

 3 Data of r , d 33 and g 33 obtained for the optimum PZT/LCT/PA and PZT/PA composites and comparison with literature data.

	Type	r	d 33 (pC/N)	g 33 (mVm/N)
	LCT/PA/0.5 PZT (present work)	73	42	65
	PA/0.5 PZT (present work)	68	28	48
	LCT/0.4 PZT [11]	30	13	48
	PVDF/0.7 PZT [16]	100	26	30
	Epoxy/0.685 PZT a

theoretical analysis is done poorly. The Lichtenecker formalism is primitive for such task and cannot be applied, if the ratio between DP of components is more than 6-7. Here this ratio is equal to at least 1000. It is also impossible to analyze pure dielectric properties without taking into account piezoelectric and elastic interactions (see, for example, Physics of the Solid State, Vol. 46, No. 12, 2004, pp. 2213-2216). The Yamada's model is almost unknown for the scientific community and was developed in 1982 year (28 years before this article). Such old models are rarely to use nowadays. I recommend to the authors to find more up-to-date literature and describe the model correctly including the description of the clamping effect by piezomeasurements.

  Sihvola's book: Electromagnetic mixing formulas and applications, ISBN 0852967721) where Lichtenecker's rule is applied and shown to hold for a ratio of 16. Moreover, some 10 years ago, a theoretical backing proof of the Lichtenecker rule was given based on effective medium theory without any restriction on permittivity ratio (J. Phys. D 31(1998)1598). Based amongst others on this paper the authors believe that the Lichtenecker rule is theoretically credible and therefore perfectly suitable as a rule of mixtures for describing the properties of the composites found in this work. Accordingly the arguments to use this model have been sharpened and incorporated in the revised text.• The article Physics of the Solid State 46(2004) 2213-2216 (as quoted by the reviewer), has no experimental backing at all and deals with an entirely different frequency range. Moreover, increased conductivity was used leading to probably unacceptable tan delta levels (not stated in that manuscript). It is evident from results of dielectric measurements presented in this paper that there is no reason to believe that any "giant response" should occur at all in this frequency range, especially since this kind of response has never actually been witnessed before. A brief discussion is introduced referring to this paper. • In response to the reviewer's statement that "the Yamada's model is almost unknown for the scientific community", the authors beg to differ because we believe this is a very relevant model. To back this view we can argue that Yamada's article has been cited no less than 90 times in Scopus (search date: 2010-06-17) by articles appearing in journals such as Appl. Phys. Lett., J. Phys. D, J. Appl. Phys. and Appl. Phys. A. It was used as the primary model describing the dielectric properties of PMN-PT powder-polymer composites in Appl. Phys. Lett. 76, 3804 (2000), a highly cited article (>180 citations in Scopus since 2000)

to reviewers report 2: Referee 2 1. Page 2. In the introduction section, the authors state that "To overcome this limitation and to process fairly flexible composites, we developed a new series of 0-3 piezoelectric composites (PZT/LCT/PA) by incorporating PZT5A4 into a matrix of LCT and polyamide (PA-11)". The authors didn't mention in the paper why/how the newly developed material PZT/LCT/PA overcomes the limitation of brittle property of PZT/LCT. Are there previous researches on PZT/LCT/PA in the literature? In the paper, the authors present the comparison of relative permittivity, piezoelectric charge constant, piezoelectric voltage coefficient of LCT/0.4PZT, LCT/PA/0.5PZT, and other piezoelectric materials in Table 2. Is the paper aimed to develop a material with high permittivity and piezoelectric constant? Please clarify the background and motivation of current work.

  table of data used is helpful and hence the data about the parameters of the components used are now given in table 2. The dc conductivity of the PZT/PA and PZT/LCT/PA composites is also measured and given in this table. Moreover, we introduced the frequency dependent conductivity in section 3.1.3. Impedance data. The text is adapted accordingly.

	Reply

  • A study on PZT/LCT composites was already done by van den Ende et al. (Van den Ende DA, Almeida de P and Van der Zwaag S 2007 J. Mater. Sci. 42 6417-6425) and this paper is referenced in the revised version of the manuscript. • The goal of the present study is indeed to develop a new composite with better permittivity and piezoelectric constant. The introductory text has been changed accordingly.

Acknowledgements

This work was financially supported by the Smartmix funding program (grant SMVA06071), as part of the program "Smart systems based on integrated Piezo". The authors are grateful to Morgan Electro Ceramics (Ruabon, United Kingdom) for providing the PZT powder used in this research and to Prof. Dr. Sybrand van der Zwaag and Dr. Theo Dingemans of Delft University of Technology for providing the LCT polymer used in this research.

We are grateful to you for reviewing our article and for the opportunity to submit the revised manuscript to Journal of Physics D: Applied Physics.

On behalf of my co-authors, With kind regards, Ir. Indu Babu. (Corresponding Author)

Babu (Ph.D Student) Laboratory of Materials and Interface Chemistry Department of Chemical Engineering and Chemistry Helix building, STO 2.28 Eindhoven University of Technology PO Box 513, 5600 MB Eindhoven, The Netherlands Tel: +31 40 247 3066 Fax: +31 40 244 5619 i.babu@tue.nl -

Our article, entitled "Processing and characterization of piezoelectric 0-3 PZT/LCT/PA composites" (Article ID: D/352960/PAP), was submitted to Journal of Physics D: Applied Physics on 3 rd April 2010. The editorial decision and reviewer's comments were returned to us on 4 th May 2010.

Revised manuscript was submitted on 22 nd July 2010 and the editorial decision was returned to us on 20 th August 2010.

I have addressed the reviewer comments in detail in the attached addenda. I have also amended the manuscript accordingly. I have highlighted the changes made in the revised manuscript.

We are grateful to you for reviewing our article and for the opportunity to submit the revised manuscript to Journal of Physics D: Applied Physics.

On behalf of my co-authors, With kind regards, Ir. Indu Babu. (Corresponding Author) ---------------------------------------------------------------------------------Ir. Indu Babu (Ph.D Student) Laboratory of Materials and Interface Chemistry Department of Chemical Engineering and Chemistry Helix building, STO 2.28 Eindhoven University of Technology PO Box 513, 5600 MB Eindhoven, The Netherlands Tel: +31 40 247 3066 Fax: +31 40 244 5619

i.babu@tue.nl ---------------------------------------------------------------------------------

Addendum:

First of all, we would like thank the reviewer for the comments and we address the various points raised in detail below.

[1] What do authors mean by d10, d50 and d90 in table 1 on page 9?

• The label d 10 , d 50 and d 90 stands for the undersize percentage of the cumulative particle size distribution. On page 8 the text has been changed accordingly. • Since the frequency of the d 33 meter is fixed at 110 Hz, the value of the relative permittivity r is also taken at the same frequency to calculate g 33 . On page 5 as well as in the legends of figures 5 and 7 the text has been changed accordingly. Since the frequencies had to be the same, we now used impedance analysis which changed the permittivity values for the 40, 50 and 60% marginally.

[3]. In subsection 3.2.1-'Impedance data': What could be reason for increase in conductivity as the volume fraction of PZT increases?

• Because interface conductivity is usually higher then bulk conductivity, the increase in the conductivity with the increase in volume fraction of PZT is attributed to the increased contribution of interface conductivity, directly related to the increasing particle volume fraction. On page 11 this text is added. • Indeed. On (now) page 13 the maximum value for d 33 is changed to 46 pC/N.

[5]. In section 2.4 "Theory": some symbols are defined multiple number of times, e.g. c , p , etc.this should be corrected.

• In section 2.4. Theory, the repetitions in c and p are removed. Only the highlighted phrase is kept.

[6]. The authors must incorporate a detailed explanation related to ananlysis of their results in the frame work of percolation theory and creation of cluster by calcinations: Using percolation theory, one can observe whether percolation threshold is reached or not. How can the authors conclude by writing -'it is clear that percolation threshold is not observed' and that' percolation theory plays a minor role'. A detailed explanation is required.

• This is complex point but a short paragraph discussing the results in the light of percolation is added in section 3.2.3.