- Email: [email protected]
Nematic Liquid Crystals: Applications
Nematic Liquid Crystals: Applications Since the 1970s liquid crystal displays based on various nematic liquid crystal modes have become the major flat panel display device and are even competing with cathode ray tubes to be the major display device. The low operating power, flexibility, and high optical quality of liquid crystal displays have resulted in their use in a wide range of consumer and commercial equipment ranging from simple monochrome watch and calculator displays to high-resolution color computer and television displays.
1. Liquid Crystal Display Construction Although liquid crystal display devices are based on different nematic liquid crystal modes a number of general constructional features are common to all the modes. Electrooptic effects in liquid crystals are produced by confining and aligning a thin layer of liquid crystal between two conducting glass substrates which have been pretreated to produce surface alignment of the liquid crystal molecules. The liquid crystal layer has an initial alignment dictated by the two substrates and this is changed by the application of a voltage across the layer; removal of the voltage restores the initial alignment. The optical properties of a thin layer of liquid crystals depend on the molecular orientation across the layer and the application of a voltage across the device, therefore, results in an electrooptic effect. The basic construction of a liquid crystal device (LCD) is shown in Fig. 1. An LCD consists of a thin layer, of 5–10 µm thickness, of liquid crystal material, confined between two glass substrates coated with a transparent conductor which has been selectively etched using standard techniques to produce the desired electrode pattern. After rigorous cleaning the inner surfaces of the substrates are treated using one of a number of chemical and mechanical techniques to produce the required surface alignment of the liquid
Figure 1 Construction of a simple liquid crystal display with electrode patterns suitable for two numbers.
crystal molecules. Heat- or UV-sensitive epoxy-based adhesives (see Thermoset Adhesies, Thermosets: Epoxies and Polyesters) are then used to seal the substrates together with a gap between them determined by glass fiber or plastic ball spacers distributed across the substrate area. The liquid crystal is introduced, typically by using a chamber that can be evacuated, through a gap in the adhesive seal; this is subsequently closed using another epoxy resin. The type of information to be displayed is predetermined by suitable patterning of the transparent electrodes. Figure 1 shows a pattern suitable for the generation of two numbers with each segment connected separately to the drive electronics. Displays are required to show a large variety of types of information (words, legends, diagrams, etc.) and the electrode pattern is designed to suit the particular image to be displayed. However, very complex images containing a large amount of information require two important changes to the simple electrode pattern shown in Fig. 1. One change involves the sharing of electrodes, a technique known as multiplexing, which reduces the number of connections between the display and the drive circuitry. Second, a dot matrix format must be used for the really high information content images found in computer monitors or television screens. This can be illustrated by way of a simple example; a small dot matrix consisting of an array of 35 dots formed from seven rows and five columns can be used to display any standard alpha numeric character. The dot matrix format is used in all computer and television screens using liquid crystals, and the drive electronics is connected to the row and column electrodes at the edge of the display. The standard VGA screen found in computer monitors provides a more realistic example of dot matrix technology, though even the VGA screen has now been largely replaced by higher resolution formats. The VGA screen contains a dot matrix array formed from 640 columns and 480 rows. There are, therefore, 307, 200 picture points (also referred to as pixels) in the VGA display which are addressed by only 1120 connections to the drive electronics. There is obviously a large amount of sharing, or multiplexing, of the electrodes in a dot matrix display and this has serious implications for the operation and performance of the display. Color is a feature of many modern LCDs and is normally generated by using a mosaic of color filters deposited within the display itself, usually adjacent to the liquid crystal to avoid errors due to parallax. Each pixel is, therefore, divided into a group of three subpixels containing red, green, and blue (RGB) color filters, with the liquid crystal behaving as an on\off switching element over each color filter. LCDs operate as either reflective or back-lit devices. The first option uses the ambient light reflected back to the viewer by a diffuse, often polarization conserving, reflector placed behind the device, whereas back-lit LCDs are illumin1
Nematic Liquid Crystals: Applications ated by a uniform source of white light placed behind the device. There is also a third option, the transflectie device, which can operate in both reflective and backlit modes depending on the ambient light level and uses a semi-transparent reflector placed behind the device.
2. Dynamic Scattering Mode The dynamic scattering mode (DSM) was used in the very first generation of LCDs introduced in 1968 (Heilmeier 1968). The DSM is now largely forgotten, unused, and of mainly historical interest. The operation of the DSM depends on a complex electrohydrodynamic effect disrupting the initial alignment of a layer of nematic liquid crystal driven by the anisotropic electrical conductivity present in nematic liquid crystals containing a suitable conductivity enhancing dopant. For a low voltage, streamline flow results in a regular array of flow patterns and as the voltage is increased the flow becomes turbulent and the random alignment of the liquid crystal strongly scatters incident light. DSM displays were introduced commercially in 1970 in watches and in 1973 in calculators. Although these early products demonstrated the tremendous potential of LCDs for producing low power, flat panel displays they exhibited a limited operating life as a result of the conducting dopants added. Reflective DSM displays were constructed using a metal layer as the back electrode of the device and usually exhibited quite low visibility as a result of the reflection of ambient lighting. The appearance of the twisted nematic (TN) mode in 1971 highlighted the inherent deficiencies of the DSM and as the initial fabrication difficulties of the TN mode were solved, it rapidly replaced the DSM as the mode of preference in LCDs.
the incident light is rotated, or guided, by the twisted liquid crystal layer, so that it emerges parallel to the transmission axis of the second polarizer, and light is transmitted. Provided that the nematic material has positive dielectric anisotropy (εR εU), the application of a small voltage of around 1–2 V between the substrates reorients the liquid crystal molecules towards the electric field, distorting the initially uniformly twisted structure. This on state no longer rotates the plane of polarization, and the light is blocked by the second polarizer. Removal of the electric field restores the uniformly twisted off state and light is again transmitted. The TN device in this configuration is known as the normally white mode. The mode can also be operated using parallel polarizers; in this case the off state is black and the configuration is known as the normally black mode. The normally white mode is invariably used in reflective displays and back-lit displays use either the normally black or the normally white modes.
3.1 Optical Properties of the Off State The normalized optical transmission TTN of the off state of a normally white TN device (i.e., using crossed polarizers) is given by (Gooch and Tarry 1974): sin# TTN l 1k
2
A
E
π\2 H B 1j F 2∆nd\λ E G 1j F 2∆nd\λ H #
E F
H
G
#
C D
"/#
(1)
G
∆nd\λ H
1
(2)
or F
The TN device has dominated the LCD industry since its invention (Schadt and Helfrich 1971) and is now often combined with thin film transistors (TFTs) and color filters to produce high-performance computer and television displays. As the name TN implies, the molecular orientation of the nematic liquid crystal in the off state twists uniformly from one substrate to the other; generally the preferred twist angle is 90m. The molecular twist is induced by the unidirectional rubbing of a thin layer of polymer coated onto the substrates and the device is assembled with the two rubbing directions set at 90m to each other. The general construction and operation of the TN mode is illustrated in Fig. 2. A pair of polarizers is used and the display will also incorporate a reflector (for a reflective display), or a back-light (for a transmissive display). In the off state, the plane of polarization of
G
F
The transmission becomes unity (i.e., TTN l 1) when either:
E
3. Twisted Nematic Mode
E
∆nd\λ H
G
#l F
E
m#k1\4 H
G
(3)
where m is an integer. The first case generally corresponds to quite thick liquid crystal layers ( 10 µm) and is known as the Mauguin limit after its discoverer. The second case is relevant for the thinner devices (" 5 µm) typical of most current commercial TN display devices, and is known as the Gooch-Tarry condition; typically m l 1 or 2.
3.2 Switching Mechanism The application of a voltage above 1–2 V reorients the liquid crystal molecules towards the direction of the electric field. However, the transition from the off to on state is not generally uniform as a result of two degeneracies known as reerse twist and reerse tilt. These produce an unacceptable patchy optical appearance unless certain precautions are taken to
Nematic Liquid Crystals: Applications remove the degeneracies. A small amount of chiral dopant is added to induce a long pitch (usually much greater than the layer thickness) resulting in a uniform twist sense for the off state. The alignment on the two substrates must also be chosen to show a slight pretilt, with the liquid crystal molecules preferably at a small angle (" 2m) to the substrate surface. However, the twist sense of the chiral dopant has to be chosen carefully to match the pretilt directions on the two substrates to obtain to totally uniform orientation in the on state and a total absence of optical patches (Raynes 1975). There is a well-defined threshold voltage above which reorientation to the on state can occur. This is given by: E
1 G
εo F εRkεU H V #c lπ# 4
3
2
1E G k j F k k2k H "" 4 $$ ## 5 6
(4) 7 8
Here εU and εR are the electric permittivities measured perpendicular and parallel to the molecular axis, respectively, k , k , and k are the splay, twist, and "" ## respectively, $$ bend elastic constants, d the liquid crystal layer thickness, and P the pitch of the liquid crystal material. Generally k " 10 pN and (εRkεU) " 10, "" of " 1 V. Figure 3 shows giving a threshold voltage transmission–voltage data for a typical TN device. The curves show the two extreme cases likely to be encountered in normal use; the transmission measured at normal incidence and 0 mC, and at 45m incidence and at 40 mC. It is evident that the transmission characteristics shift significantly between these two extreme cases. The full solution of the free energy equations produces detailed information on the orientation across the layer in the on state. The combination of these results with optical methods allows very detailed modeling of both the static and dynamic switching properties of the TN mode to be made (Berreman 1983). 3.3 Multiplexed Twisted Nematic Deices Simple TN displays showing only a small amount of information have direct electrical connections between each pixel and the drive electronics. As the information content of a display increases it becomes impossible to address each pixel individually and multiplexing (matrix addressing) is used. Each row in the matrix is selected sequentially and appropriate data waveforms are applied to the columns. The slow response times of LCDs (of the order of tens of milliseconds) means that each pixel responds to the root mean square (RMS) of the resulting waveforms. As the number of rows (n) in the matrix increases, the fraction (1\n) of the total time for which the selected pixels see the full select pulse
Figure 2 Operation of the TN mode.
decreases, thereby reducing the ratio of the RMS voltages seen by the selected (on) and the unselected (off) pixels. Alt and Pleshko (1975) showed that the maximum ratio of select to unselected RMS voltages is given by: Vsel l Vunsel
A
Nnj1 Nnk1 B
C
"/#
(5)
D
90 0°C (normal) Transmission (%)
j2k d\P ##
40 °C (45°)
10 0
1 2 Applied voltage (V)
3
Figure 3 Voltage dependence of the TN mode at normal incidence at 0 mC, and at oblique incidence (45m) and 40 mC.
3
Nematic Liquid Crystals: Applications For a matrix containing 100 rows (i.e., n l 100), this ratio is only 1.11 and the effective RMS select voltage is only 11% higher than the effective RMS voltage on unselected pixels. The size of the matrix it is possible to address (i.e., the maximum value of n) is, therefore, determined by the steepness of the transmission– voltage curve of the mode. It is obvious from Fig. 3 that the transmission– voltage curve of the TN mode is not particularly steep and is made even worse when angular and temperature effects are considered. The theoretical slope of the reorientation of a TN device just above threshold has been shown (Raynes 1998) to be proportional to the expression: E
G
VkVc H \Vc (6) E G 5k \8k j F εRkεU H \εU $$ "" From Eqn. (6) it is evident that lowering either k \k $$ "" or (εRkεU)\εU, will increase the slope above threshold. However, the scope for reducing (εRkεU)\εU is limited by the resulting increase of threshold voltage seen from Eqn. (4), and lowering the ratio k \k represents $$ multiplexing "" the only viable option for improving the performance of TN devices. The most efficient way of reducing k \k in liquid crystal materials is by using $$ "" of terminal cyano and noncyano a combination materials (Bradshaw et al. 1984). For terminal cyano compounds such as the well-known cyano biphenyls (CB) and phenyl cyclohexane compounds (PCH) the values of k \k lie within the range 1.5–2.5. The "" addition of$$around 30 wt.% of a nonpolar liquid crystal without a terminal cyano group lowers this ratio to 1.0–1.4, producing a significant improvement in the multiplexing performance. Such combinations, known as hybrid mixtures, tend to also demonstrate the improved temperature dependence helpful for multiplexed displays. The amount of chiral dopant added to produce uniform switching in the device also affects the multiplexing performance of the device. Too much chiral dopant induces a deterioration in the multiplexing performance, and the amount is kept as small as possible consistent with uniform switching. Typically the value of the pitch used is such that P 200 µm. However, even with all these improvements in device and liquid crystal material design, passive matrix addressing of TN displays is generally limited to about 20 rows of electrodes, corresponding to only two to three rows of alpha numeric characters. The simple TN displays found in watches and calculators are normally addressed using passive matrix addressing techniques. These simple displays are topologically equivalent to dot matrices with two to four rows (i.e., Vsel\Vunsel " 2) and perform perfectly adequately. However, for more complex displays showing images of increased resolution, the performance of the passive matrix addressed TN display rapidly falls away and becomes totally unacceptable for computer and teleslopeTN `
4
F
vision images. Two quite different extensions of the basic TN mode are used to display high-resolution images: the TFT LCD and the supertwisted nematic (STN) LCD. Displays based on these two modes are now ubiquitous in a wide range of applications such as instrumentation, mobile phones, computer monitors, and television screens. 4. Thin Film Transistor Displays The limitations of passive matrix addressing can be overcome by the integration of a nonlinear electronic device at each pixel. This device serves to greatly increase the effective Vsel\Vunsel ratio appearing at each pixel and removes the limitations imposed by the finite slope of the transmission–voltage curve of the liquid crystal mode. Although a number of active and passive electronic devices have been investigated as nonlinear devices, the technology has focussed around the use of TFTs fabricated using amorphous silicon (α-Si) as the semiconducting material. Conventional crystalline silicon is used for small displays of around 2 cm in size known as micro-displays. Large area, direct view displays use amorphous silicon because of the ease with which it can be deposited over large areas. Early TFT displays were fabricated using CdSe, but following the successful demonstration by Snell et al. (1981), α-Si has become the material of choice. Figure 4 shows the active substrate of a TFT LCD with a TFT at each pixel linking the series of gate lines and drain lines. A voltage is applied to each gate line in sequence switching on the TFTs in that line to allow the voltages on each drain line to be transferred to the pixels. As the addressing sequence proceeds, the TFTs in that line are switched off and the pixels become electrically isolated. An additional capacitor can be added at each pixel to help increase the RC time constant of the pixel to make it compatible with the frame time for the complete addressing cycle. The RC time constant of the pixel is also increased by choosing liquid crystal materials with low electrical conductivity. So critical is this requirement that it rules out the use of previously popular nematic liquid crystals containing terminal cyano groups (CB and PCH) to produce the positive dielectric anisotropy (εR εU). In their place a number of nematic materials have been developed which incorporate terminal fluorine atoms to produce materials with adequate dielectric anisotropy together with very low electrical conductivities. The majority of TFT displays use the TN mode. Carefully designed compensation films are added to improve the rather poor viewing angle characteristics of the TFT-TN displays. It is also possible to subdivide each pixel to improve the poor viewing angle characteristics evident in Fig. 3. TFT-TN displays are now widely used in portable computers, increasingly as monitors for desktop computers and as television displays. Performance is generally excellent except for
Transmission
Nematic Liquid Crystals: Applications
Voltage
Figure 5 Voltage dependence of the transmission of supertwisted twisted layers of liquid crystals.
Figure 4 Active substrate of a TFT-TN display.
some blurring that occurs with fast moving video images. This is as much the consequence of the row at a time addressing than the inherent response times of the TN mode. The prime limitation of TFT LCDs is the difficulty and cost of fabricating really large displays and only displays with diagonal sizes up to around 50 cm are commercially available. Diagonal sizes up to 75 and 100 cm are likely to remain expensive because of the difficulties of fabricating TFT arrays over these large areas.
this twist angle lies between 225m and 270m); the precise value of this twist angle depends on the physical properties of the liquid crystal material used and the layer geometry. Extension of Eqn. (6) to the more general case shows that the initial slope of an STN layer is approximately proportional to: slopeSTN ` 3
2
1
4
5. Supertwisted Nematic Mode Equation (5) shows that as the number of rows in a dot matrix, n, is increased, the ratio Vsel\Vunsel becomes too small to produce adequate contrast between pixels in a TN display. However, the steepness of the transmission–voltage curve can be improved by the simple method of increasing the twist angle (φ) of the liquid crystal layer from the 90m found in TN devices to lie within the range 180–270m (Waters et al. 1983). This is illustrated by the transmission–voltage curves shown in Fig. 5 for layers of a standard nematic liquid crystal mixture with a range of twist angles. Increasing the twist angle improves the slope, and, hence, the performance with passive matrix addressing, until eventually the curve becomes bistable. This is evident in Fig. 5 for a 270m twist angle. The larger twist angles are stabilized by a combination of surface alignment and chiral dopant and the ratio of the thickness to pitch (d\P) should lie within the range: φ\2πk0.25 (d\P) φ\2πj0.25
(7)
The slope of the transmission curve is almost infinite for a particular twist angle (for the material in Fig. 5
(VkVc)\Vc 5 k kCφ# 6 $$ 7 j(εRkεU)\εU k jDφ# 8 ""
(8)
where C and D are combinations of the elastic constants of the liquid crystal and are both positive for most known nematic materials. From Eqn. (8) it can be seen that the denominator decreases as φ increases, and the slope approaches infinity for a specific value of φ. Numerical modeling confirms this picture and can be used for more accurate device and material optimization. As the twist angle φ of the layer is increased, the larger values of (d\P) required (Eqn. (7)) make other field-induced periodic instabilities possible, and these compete with the uniform reorientation process described above. Eventually a spatially modulated instability appears as a striped or scattering texture degrading the appearance of the display. These periodic distortions are minimized by the use of medium surface pretilt angles (5–10m) and small d\P ratios; this tends to restrict the useful range of φ to 180–270m. The optical properties of STN devices have been optimized using two polarizers (Scheffer and Nehring 1985) to produce medium-performance devices with contrast ratios in excess of 10: 1. These STN devices have found widespread use where price, rather than performance, is at a premium, and are widely used in portable and laboratory equipment, mobile phones, and computer terminals. 5
Nematic Liquid Crystals: Applications 5.1 Optical Properties of the STN Mode The optical properties of the STN mode are subtly different from the TN mode. The most obvious optical feature of the STN mode is a coloration in the off state resulting in displays with an easily recognized bright yellow\green hue. Full modeling of the optics of STN displays has been carried out by a number of authors, however, a simple extension of the analytical techniques for the TN mode give useful insight into the optical properties of the STN mode (Raynes 1998). The detailed results depend on the precise orientation of the two polarizers, but the case of the one polarizer oriented at an angle of j45m to the input director and the other at an angle of j45m to the exit director can be considered as an illustrative example. The normalized transmission TSTN is given by: TSTN l cos#Nφ#j(∆ndπ\λ#)
(9)
and the wavelength dependence of TSTN results in a colored device with a maximum transmission (TSTN l 1) when ∆nd\λ l Np#k(φ\π)#
(10)
where p is an integer. The optimum, values of (∆nd ), the transmission spectra and characteristic colors of a range of STN devices are readily derived by considering the more general case of Eqn. (9). The color inherent in STN devices can pose a problem for many applications, for example their use in RGB color displays, and two principle techniques have been found to remove this color and produce black and white electrooptic effects suitable for RGB color displays. The first method of color compensation involves the use of a second unswitched STN layer which is offset by 90m and twists the opposite way, but otherwise is identical to the first layer. This double layer STN combination is optically neutral and the off state appears either black or white depending on the polarizer orientations. The second method of optical compensation involves the inclusion of plastic birefringent films between the polarizers and the STN layer. Recent developments include the use of multiple retardation films, wavelength-dependent retardation films and combinations of biaxial and uniaxial films. Both compensation techniques affect only the coloration of the off state.
6. Alternative Nematic Liquid Crystal Modes Currently the LCD market is dominated by displays based on the TN, TFT-TN, and STN modes. However, a number of alternative display modes based on nematic liquid crystals are starting to appear in the market place, and yet more are being actively studied in research groups around the world. 6
Several of these alternative nematic liquid crystal modes are designed to replace the TN mode with TFT arrays. Direct view devices which are back-lit are very demanding on the performance of the liquid crystal mode, particularly the viewing angle characteristics. The in-plane switching (IPS) nematic mode has outstanding viewing angle characteristics as a result of the orientation of the liquid crystal molecules always being parallel to the substrates. Switching is achieved by the application of voltages to one substrate only, and an in-plane electric field induces in-plane switching. The IPS mode tends to be less efficient with the use of light because of the complexity of the electrode patterns required to generate the in-plane electric field. The ertically aligned nematic (VAN) mode is a second development also appearing in commercial displays. A number of variants exist, but all have a similar off state in which the liquid crystal molecules are aligned normal to the two substrates. Liquid crystal materials with negative dielectric anisotropy (εR εU) are used and the application of an electric field across the liquid crystal layer changes the molecular orientation to lie parallel to the substrates. The VAN mode generally exhibits good viewing angle characteristics and has the added benefit of showing response times slightly faster than the conventional TN mode. A third mode recently developed for TFT arrays is the single polarizer mode now being used for reflective color displays for portable games. This mode uses a single polarizer together with a polarizationconserving reflector deposited on the lower substrate. A liquid crystal material with positive dielectric anisotropy (εR εU) is aligned with the molecular axes in the off state parallel to the substrates and is re-aligned to become orthogonal to the substrates in the on state. Optical performance is improved by using a moderate twist angle of around 60m and by using extra retardation films between the polarizer and the liquid crystal. Bistable displays represent another area where alternative nematic-based modes are appearing. Many display applications do not require a rapidly changing image and they would benefit from a display that remains visible even after the power is removed, extending the life of the battery. The surface stabilized cholesteric texture (SSCT) is one such mode which also has the added benefit of a high reflectivity making it suitable for operation without a power consuming back-light. In the SSCT mode a nematic liquid crystal is doped with enough chiral dopant to generate a pitch short enough to reflect visible light. The off state is, therefore, strongly reflective with a color controlled by the amount of chiral dopant. The application of an electric field switches the orientation to another bistable state which is not reflective but slightly scattering, and the incident light is absorbed by a suitable layer placed behind the device. The zenithal bistable deice (ZBD) is another bistable nematic mode. Gratings are deposited onto the glass substrates
Nematic Liquid Crystals: Applications to induce a bistable alignment of the nematic liquid crystal which subsequently generates an image using two polarizers in a conventional manner. Both the SSCT and ZBD modes use higher voltages than the conventional TN mode, but are regarded as strong candidates for future bistable device applications. See also: Liquid Crystals: Overview; Calamitic Liquid Crystals; Nematic Liquid Crystals: Elastic Properties; Liquid Crystals, Molecular Design of : Calamitics Bibliography Alt P M, Pleshko P 1975 Scanning limitations of liquid crystal displays. IEEE Trans. Electron. De. 21, 146–55 Bahadur B (ed.) 1990 Liquid Crystals Applications and Uses. World Scientific, Singapore Berreman D W 1983 Numerical modelling of twisted nematic devices. In: Hilsum C, Raynes E P (eds.) Liquid Crystals: Their Physics, Chemistry and Applications. The Royal Society, London Bradshaw M J, Raynes E P, Fedak I, Leadbetter A J 1984 A correlation between short range smectic-like ordering and the elastic constants of nematic liquid crystals. J. Phys. 45, 157–62
Chandrasekhar S 1992 Liquid Crystals. Cambridge University Press, Cambridge de Gennes P G, Prost J 1993 The Physics of Liquid Crystals. Oxford University Press, Oxford Gooch C H, Tarry H A 1974 Optical characteristics of twisted nematic liquid crystal films. Electron. Lett. 10, 2–4 Heilmeier G H 1968 Dynamic scattering. Proc. IEEE 56, 1162–71 Raynes E P 1975 Optically active additives in twisted nematic devices. Re. Phys. Appl. 10, 117–20 Raynes E P 1998 Nematic and supertwisted nematic liquid crystal displays. In: Elston S J, Sambles J R (eds.) The Optics of Thermotropic Liquid Crystals. Taylor and Francis, London Schadt M, Helfrich W 1971 Voltage-dependent optical activity of a twisted nematic liquid crystal. Appl. Phys. Lett. 18, 127–8 Scheffer T J, Nehring J 1984 A new, highly multiplexable liquid crystal display. Appl. Phys. Lett. 45, 1021–3 Snell A J, Mackenzie K D, Spear W E, LeComber P G, Hughes A J 1981 Applications of amorphous Si FETs in addressable LCD panels. Appl. Phys. 24, 357–62 Waters C M, Brimmell V, Raynes E P 1983 Highly multiplexable dyed LCDs. Proc. 3rd Int. Display Res. Conf. Kobe, Japan
E. P. Raynes
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 6058–6065 7
1. Liquid Crystal Display Construction Although liquid crystal display devices are based on different nematic liquid crystal modes a number of general constructional features are common to all the modes. Electrooptic effects in liquid crystals are produced by confining and aligning a thin layer of liquid crystal between two conducting glass substrates which have been pretreated to produce surface alignment of the liquid crystal molecules. The liquid crystal layer has an initial alignment dictated by the two substrates and this is changed by the application of a voltage across the layer; removal of the voltage restores the initial alignment. The optical properties of a thin layer of liquid crystals depend on the molecular orientation across the layer and the application of a voltage across the device, therefore, results in an electrooptic effect. The basic construction of a liquid crystal device (LCD) is shown in Fig. 1. An LCD consists of a thin layer, of 5–10 µm thickness, of liquid crystal material, confined between two glass substrates coated with a transparent conductor which has been selectively etched using standard techniques to produce the desired electrode pattern. After rigorous cleaning the inner surfaces of the substrates are treated using one of a number of chemical and mechanical techniques to produce the required surface alignment of the liquid
Figure 1 Construction of a simple liquid crystal display with electrode patterns suitable for two numbers.
crystal molecules. Heat- or UV-sensitive epoxy-based adhesives (see Thermoset Adhesies, Thermosets: Epoxies and Polyesters) are then used to seal the substrates together with a gap between them determined by glass fiber or plastic ball spacers distributed across the substrate area. The liquid crystal is introduced, typically by using a chamber that can be evacuated, through a gap in the adhesive seal; this is subsequently closed using another epoxy resin. The type of information to be displayed is predetermined by suitable patterning of the transparent electrodes. Figure 1 shows a pattern suitable for the generation of two numbers with each segment connected separately to the drive electronics. Displays are required to show a large variety of types of information (words, legends, diagrams, etc.) and the electrode pattern is designed to suit the particular image to be displayed. However, very complex images containing a large amount of information require two important changes to the simple electrode pattern shown in Fig. 1. One change involves the sharing of electrodes, a technique known as multiplexing, which reduces the number of connections between the display and the drive circuitry. Second, a dot matrix format must be used for the really high information content images found in computer monitors or television screens. This can be illustrated by way of a simple example; a small dot matrix consisting of an array of 35 dots formed from seven rows and five columns can be used to display any standard alpha numeric character. The dot matrix format is used in all computer and television screens using liquid crystals, and the drive electronics is connected to the row and column electrodes at the edge of the display. The standard VGA screen found in computer monitors provides a more realistic example of dot matrix technology, though even the VGA screen has now been largely replaced by higher resolution formats. The VGA screen contains a dot matrix array formed from 640 columns and 480 rows. There are, therefore, 307, 200 picture points (also referred to as pixels) in the VGA display which are addressed by only 1120 connections to the drive electronics. There is obviously a large amount of sharing, or multiplexing, of the electrodes in a dot matrix display and this has serious implications for the operation and performance of the display. Color is a feature of many modern LCDs and is normally generated by using a mosaic of color filters deposited within the display itself, usually adjacent to the liquid crystal to avoid errors due to parallax. Each pixel is, therefore, divided into a group of three subpixels containing red, green, and blue (RGB) color filters, with the liquid crystal behaving as an on\off switching element over each color filter. LCDs operate as either reflective or back-lit devices. The first option uses the ambient light reflected back to the viewer by a diffuse, often polarization conserving, reflector placed behind the device, whereas back-lit LCDs are illumin1
Nematic Liquid Crystals: Applications ated by a uniform source of white light placed behind the device. There is also a third option, the transflectie device, which can operate in both reflective and backlit modes depending on the ambient light level and uses a semi-transparent reflector placed behind the device.
2. Dynamic Scattering Mode The dynamic scattering mode (DSM) was used in the very first generation of LCDs introduced in 1968 (Heilmeier 1968). The DSM is now largely forgotten, unused, and of mainly historical interest. The operation of the DSM depends on a complex electrohydrodynamic effect disrupting the initial alignment of a layer of nematic liquid crystal driven by the anisotropic electrical conductivity present in nematic liquid crystals containing a suitable conductivity enhancing dopant. For a low voltage, streamline flow results in a regular array of flow patterns and as the voltage is increased the flow becomes turbulent and the random alignment of the liquid crystal strongly scatters incident light. DSM displays were introduced commercially in 1970 in watches and in 1973 in calculators. Although these early products demonstrated the tremendous potential of LCDs for producing low power, flat panel displays they exhibited a limited operating life as a result of the conducting dopants added. Reflective DSM displays were constructed using a metal layer as the back electrode of the device and usually exhibited quite low visibility as a result of the reflection of ambient lighting. The appearance of the twisted nematic (TN) mode in 1971 highlighted the inherent deficiencies of the DSM and as the initial fabrication difficulties of the TN mode were solved, it rapidly replaced the DSM as the mode of preference in LCDs.
the incident light is rotated, or guided, by the twisted liquid crystal layer, so that it emerges parallel to the transmission axis of the second polarizer, and light is transmitted. Provided that the nematic material has positive dielectric anisotropy (εR εU), the application of a small voltage of around 1–2 V between the substrates reorients the liquid crystal molecules towards the electric field, distorting the initially uniformly twisted structure. This on state no longer rotates the plane of polarization, and the light is blocked by the second polarizer. Removal of the electric field restores the uniformly twisted off state and light is again transmitted. The TN device in this configuration is known as the normally white mode. The mode can also be operated using parallel polarizers; in this case the off state is black and the configuration is known as the normally black mode. The normally white mode is invariably used in reflective displays and back-lit displays use either the normally black or the normally white modes.
3.1 Optical Properties of the Off State The normalized optical transmission TTN of the off state of a normally white TN device (i.e., using crossed polarizers) is given by (Gooch and Tarry 1974): sin# TTN l 1k
2
A
E
π\2 H B 1j F 2∆nd\λ E G 1j F 2∆nd\λ H #
E F
H
G
#
C D
"/#
(1)
G
∆nd\λ H
1
(2)
or F
The TN device has dominated the LCD industry since its invention (Schadt and Helfrich 1971) and is now often combined with thin film transistors (TFTs) and color filters to produce high-performance computer and television displays. As the name TN implies, the molecular orientation of the nematic liquid crystal in the off state twists uniformly from one substrate to the other; generally the preferred twist angle is 90m. The molecular twist is induced by the unidirectional rubbing of a thin layer of polymer coated onto the substrates and the device is assembled with the two rubbing directions set at 90m to each other. The general construction and operation of the TN mode is illustrated in Fig. 2. A pair of polarizers is used and the display will also incorporate a reflector (for a reflective display), or a back-light (for a transmissive display). In the off state, the plane of polarization of
G
F
The transmission becomes unity (i.e., TTN l 1) when either:
E
3. Twisted Nematic Mode
E
∆nd\λ H
G
#l F
E
m#k1\4 H
G
(3)
where m is an integer. The first case generally corresponds to quite thick liquid crystal layers ( 10 µm) and is known as the Mauguin limit after its discoverer. The second case is relevant for the thinner devices (" 5 µm) typical of most current commercial TN display devices, and is known as the Gooch-Tarry condition; typically m l 1 or 2.
3.2 Switching Mechanism The application of a voltage above 1–2 V reorients the liquid crystal molecules towards the direction of the electric field. However, the transition from the off to on state is not generally uniform as a result of two degeneracies known as reerse twist and reerse tilt. These produce an unacceptable patchy optical appearance unless certain precautions are taken to
Nematic Liquid Crystals: Applications remove the degeneracies. A small amount of chiral dopant is added to induce a long pitch (usually much greater than the layer thickness) resulting in a uniform twist sense for the off state. The alignment on the two substrates must also be chosen to show a slight pretilt, with the liquid crystal molecules preferably at a small angle (" 2m) to the substrate surface. However, the twist sense of the chiral dopant has to be chosen carefully to match the pretilt directions on the two substrates to obtain to totally uniform orientation in the on state and a total absence of optical patches (Raynes 1975). There is a well-defined threshold voltage above which reorientation to the on state can occur. This is given by: E
1 G
εo F εRkεU H V #c lπ# 4
3
2
1E G k j F k k2k H "" 4 $$ ## 5 6
(4) 7 8
Here εU and εR are the electric permittivities measured perpendicular and parallel to the molecular axis, respectively, k , k , and k are the splay, twist, and "" ## respectively, $$ bend elastic constants, d the liquid crystal layer thickness, and P the pitch of the liquid crystal material. Generally k " 10 pN and (εRkεU) " 10, "" of " 1 V. Figure 3 shows giving a threshold voltage transmission–voltage data for a typical TN device. The curves show the two extreme cases likely to be encountered in normal use; the transmission measured at normal incidence and 0 mC, and at 45m incidence and at 40 mC. It is evident that the transmission characteristics shift significantly between these two extreme cases. The full solution of the free energy equations produces detailed information on the orientation across the layer in the on state. The combination of these results with optical methods allows very detailed modeling of both the static and dynamic switching properties of the TN mode to be made (Berreman 1983). 3.3 Multiplexed Twisted Nematic Deices Simple TN displays showing only a small amount of information have direct electrical connections between each pixel and the drive electronics. As the information content of a display increases it becomes impossible to address each pixel individually and multiplexing (matrix addressing) is used. Each row in the matrix is selected sequentially and appropriate data waveforms are applied to the columns. The slow response times of LCDs (of the order of tens of milliseconds) means that each pixel responds to the root mean square (RMS) of the resulting waveforms. As the number of rows (n) in the matrix increases, the fraction (1\n) of the total time for which the selected pixels see the full select pulse
Figure 2 Operation of the TN mode.
decreases, thereby reducing the ratio of the RMS voltages seen by the selected (on) and the unselected (off) pixels. Alt and Pleshko (1975) showed that the maximum ratio of select to unselected RMS voltages is given by: Vsel l Vunsel
A
Nnj1 Nnk1 B
C
"/#
(5)
D
90 0°C (normal) Transmission (%)
j2k d\P ##
40 °C (45°)
10 0
1 2 Applied voltage (V)
3
Figure 3 Voltage dependence of the TN mode at normal incidence at 0 mC, and at oblique incidence (45m) and 40 mC.
3
Nematic Liquid Crystals: Applications For a matrix containing 100 rows (i.e., n l 100), this ratio is only 1.11 and the effective RMS select voltage is only 11% higher than the effective RMS voltage on unselected pixels. The size of the matrix it is possible to address (i.e., the maximum value of n) is, therefore, determined by the steepness of the transmission– voltage curve of the mode. It is obvious from Fig. 3 that the transmission– voltage curve of the TN mode is not particularly steep and is made even worse when angular and temperature effects are considered. The theoretical slope of the reorientation of a TN device just above threshold has been shown (Raynes 1998) to be proportional to the expression: E
G
VkVc H \Vc (6) E G 5k \8k j F εRkεU H \εU $$ "" From Eqn. (6) it is evident that lowering either k \k $$ "" or (εRkεU)\εU, will increase the slope above threshold. However, the scope for reducing (εRkεU)\εU is limited by the resulting increase of threshold voltage seen from Eqn. (4), and lowering the ratio k \k represents $$ multiplexing "" the only viable option for improving the performance of TN devices. The most efficient way of reducing k \k in liquid crystal materials is by using $$ "" of terminal cyano and noncyano a combination materials (Bradshaw et al. 1984). For terminal cyano compounds such as the well-known cyano biphenyls (CB) and phenyl cyclohexane compounds (PCH) the values of k \k lie within the range 1.5–2.5. The "" addition of$$around 30 wt.% of a nonpolar liquid crystal without a terminal cyano group lowers this ratio to 1.0–1.4, producing a significant improvement in the multiplexing performance. Such combinations, known as hybrid mixtures, tend to also demonstrate the improved temperature dependence helpful for multiplexed displays. The amount of chiral dopant added to produce uniform switching in the device also affects the multiplexing performance of the device. Too much chiral dopant induces a deterioration in the multiplexing performance, and the amount is kept as small as possible consistent with uniform switching. Typically the value of the pitch used is such that P 200 µm. However, even with all these improvements in device and liquid crystal material design, passive matrix addressing of TN displays is generally limited to about 20 rows of electrodes, corresponding to only two to three rows of alpha numeric characters. The simple TN displays found in watches and calculators are normally addressed using passive matrix addressing techniques. These simple displays are topologically equivalent to dot matrices with two to four rows (i.e., Vsel\Vunsel " 2) and perform perfectly adequately. However, for more complex displays showing images of increased resolution, the performance of the passive matrix addressed TN display rapidly falls away and becomes totally unacceptable for computer and teleslopeTN `
4
F
vision images. Two quite different extensions of the basic TN mode are used to display high-resolution images: the TFT LCD and the supertwisted nematic (STN) LCD. Displays based on these two modes are now ubiquitous in a wide range of applications such as instrumentation, mobile phones, computer monitors, and television screens. 4. Thin Film Transistor Displays The limitations of passive matrix addressing can be overcome by the integration of a nonlinear electronic device at each pixel. This device serves to greatly increase the effective Vsel\Vunsel ratio appearing at each pixel and removes the limitations imposed by the finite slope of the transmission–voltage curve of the liquid crystal mode. Although a number of active and passive electronic devices have been investigated as nonlinear devices, the technology has focussed around the use of TFTs fabricated using amorphous silicon (α-Si) as the semiconducting material. Conventional crystalline silicon is used for small displays of around 2 cm in size known as micro-displays. Large area, direct view displays use amorphous silicon because of the ease with which it can be deposited over large areas. Early TFT displays were fabricated using CdSe, but following the successful demonstration by Snell et al. (1981), α-Si has become the material of choice. Figure 4 shows the active substrate of a TFT LCD with a TFT at each pixel linking the series of gate lines and drain lines. A voltage is applied to each gate line in sequence switching on the TFTs in that line to allow the voltages on each drain line to be transferred to the pixels. As the addressing sequence proceeds, the TFTs in that line are switched off and the pixels become electrically isolated. An additional capacitor can be added at each pixel to help increase the RC time constant of the pixel to make it compatible with the frame time for the complete addressing cycle. The RC time constant of the pixel is also increased by choosing liquid crystal materials with low electrical conductivity. So critical is this requirement that it rules out the use of previously popular nematic liquid crystals containing terminal cyano groups (CB and PCH) to produce the positive dielectric anisotropy (εR εU). In their place a number of nematic materials have been developed which incorporate terminal fluorine atoms to produce materials with adequate dielectric anisotropy together with very low electrical conductivities. The majority of TFT displays use the TN mode. Carefully designed compensation films are added to improve the rather poor viewing angle characteristics of the TFT-TN displays. It is also possible to subdivide each pixel to improve the poor viewing angle characteristics evident in Fig. 3. TFT-TN displays are now widely used in portable computers, increasingly as monitors for desktop computers and as television displays. Performance is generally excellent except for
Transmission
Nematic Liquid Crystals: Applications
Voltage
Figure 5 Voltage dependence of the transmission of supertwisted twisted layers of liquid crystals.
Figure 4 Active substrate of a TFT-TN display.
some blurring that occurs with fast moving video images. This is as much the consequence of the row at a time addressing than the inherent response times of the TN mode. The prime limitation of TFT LCDs is the difficulty and cost of fabricating really large displays and only displays with diagonal sizes up to around 50 cm are commercially available. Diagonal sizes up to 75 and 100 cm are likely to remain expensive because of the difficulties of fabricating TFT arrays over these large areas.
this twist angle lies between 225m and 270m); the precise value of this twist angle depends on the physical properties of the liquid crystal material used and the layer geometry. Extension of Eqn. (6) to the more general case shows that the initial slope of an STN layer is approximately proportional to: slopeSTN ` 3
2
1
4
5. Supertwisted Nematic Mode Equation (5) shows that as the number of rows in a dot matrix, n, is increased, the ratio Vsel\Vunsel becomes too small to produce adequate contrast between pixels in a TN display. However, the steepness of the transmission–voltage curve can be improved by the simple method of increasing the twist angle (φ) of the liquid crystal layer from the 90m found in TN devices to lie within the range 180–270m (Waters et al. 1983). This is illustrated by the transmission–voltage curves shown in Fig. 5 for layers of a standard nematic liquid crystal mixture with a range of twist angles. Increasing the twist angle improves the slope, and, hence, the performance with passive matrix addressing, until eventually the curve becomes bistable. This is evident in Fig. 5 for a 270m twist angle. The larger twist angles are stabilized by a combination of surface alignment and chiral dopant and the ratio of the thickness to pitch (d\P) should lie within the range: φ\2πk0.25 (d\P) φ\2πj0.25
(7)
The slope of the transmission curve is almost infinite for a particular twist angle (for the material in Fig. 5
(VkVc)\Vc 5 k kCφ# 6 $$ 7 j(εRkεU)\εU k jDφ# 8 ""
(8)
where C and D are combinations of the elastic constants of the liquid crystal and are both positive for most known nematic materials. From Eqn. (8) it can be seen that the denominator decreases as φ increases, and the slope approaches infinity for a specific value of φ. Numerical modeling confirms this picture and can be used for more accurate device and material optimization. As the twist angle φ of the layer is increased, the larger values of (d\P) required (Eqn. (7)) make other field-induced periodic instabilities possible, and these compete with the uniform reorientation process described above. Eventually a spatially modulated instability appears as a striped or scattering texture degrading the appearance of the display. These periodic distortions are minimized by the use of medium surface pretilt angles (5–10m) and small d\P ratios; this tends to restrict the useful range of φ to 180–270m. The optical properties of STN devices have been optimized using two polarizers (Scheffer and Nehring 1985) to produce medium-performance devices with contrast ratios in excess of 10: 1. These STN devices have found widespread use where price, rather than performance, is at a premium, and are widely used in portable and laboratory equipment, mobile phones, and computer terminals. 5
Nematic Liquid Crystals: Applications 5.1 Optical Properties of the STN Mode The optical properties of the STN mode are subtly different from the TN mode. The most obvious optical feature of the STN mode is a coloration in the off state resulting in displays with an easily recognized bright yellow\green hue. Full modeling of the optics of STN displays has been carried out by a number of authors, however, a simple extension of the analytical techniques for the TN mode give useful insight into the optical properties of the STN mode (Raynes 1998). The detailed results depend on the precise orientation of the two polarizers, but the case of the one polarizer oriented at an angle of j45m to the input director and the other at an angle of j45m to the exit director can be considered as an illustrative example. The normalized transmission TSTN is given by: TSTN l cos#Nφ#j(∆ndπ\λ#)
(9)
and the wavelength dependence of TSTN results in a colored device with a maximum transmission (TSTN l 1) when ∆nd\λ l Np#k(φ\π)#
(10)
where p is an integer. The optimum, values of (∆nd ), the transmission spectra and characteristic colors of a range of STN devices are readily derived by considering the more general case of Eqn. (9). The color inherent in STN devices can pose a problem for many applications, for example their use in RGB color displays, and two principle techniques have been found to remove this color and produce black and white electrooptic effects suitable for RGB color displays. The first method of color compensation involves the use of a second unswitched STN layer which is offset by 90m and twists the opposite way, but otherwise is identical to the first layer. This double layer STN combination is optically neutral and the off state appears either black or white depending on the polarizer orientations. The second method of optical compensation involves the inclusion of plastic birefringent films between the polarizers and the STN layer. Recent developments include the use of multiple retardation films, wavelength-dependent retardation films and combinations of biaxial and uniaxial films. Both compensation techniques affect only the coloration of the off state.
6. Alternative Nematic Liquid Crystal Modes Currently the LCD market is dominated by displays based on the TN, TFT-TN, and STN modes. However, a number of alternative display modes based on nematic liquid crystals are starting to appear in the market place, and yet more are being actively studied in research groups around the world. 6
Several of these alternative nematic liquid crystal modes are designed to replace the TN mode with TFT arrays. Direct view devices which are back-lit are very demanding on the performance of the liquid crystal mode, particularly the viewing angle characteristics. The in-plane switching (IPS) nematic mode has outstanding viewing angle characteristics as a result of the orientation of the liquid crystal molecules always being parallel to the substrates. Switching is achieved by the application of voltages to one substrate only, and an in-plane electric field induces in-plane switching. The IPS mode tends to be less efficient with the use of light because of the complexity of the electrode patterns required to generate the in-plane electric field. The ertically aligned nematic (VAN) mode is a second development also appearing in commercial displays. A number of variants exist, but all have a similar off state in which the liquid crystal molecules are aligned normal to the two substrates. Liquid crystal materials with negative dielectric anisotropy (εR εU) are used and the application of an electric field across the liquid crystal layer changes the molecular orientation to lie parallel to the substrates. The VAN mode generally exhibits good viewing angle characteristics and has the added benefit of showing response times slightly faster than the conventional TN mode. A third mode recently developed for TFT arrays is the single polarizer mode now being used for reflective color displays for portable games. This mode uses a single polarizer together with a polarizationconserving reflector deposited on the lower substrate. A liquid crystal material with positive dielectric anisotropy (εR εU) is aligned with the molecular axes in the off state parallel to the substrates and is re-aligned to become orthogonal to the substrates in the on state. Optical performance is improved by using a moderate twist angle of around 60m and by using extra retardation films between the polarizer and the liquid crystal. Bistable displays represent another area where alternative nematic-based modes are appearing. Many display applications do not require a rapidly changing image and they would benefit from a display that remains visible even after the power is removed, extending the life of the battery. The surface stabilized cholesteric texture (SSCT) is one such mode which also has the added benefit of a high reflectivity making it suitable for operation without a power consuming back-light. In the SSCT mode a nematic liquid crystal is doped with enough chiral dopant to generate a pitch short enough to reflect visible light. The off state is, therefore, strongly reflective with a color controlled by the amount of chiral dopant. The application of an electric field switches the orientation to another bistable state which is not reflective but slightly scattering, and the incident light is absorbed by a suitable layer placed behind the device. The zenithal bistable deice (ZBD) is another bistable nematic mode. Gratings are deposited onto the glass substrates
Nematic Liquid Crystals: Applications to induce a bistable alignment of the nematic liquid crystal which subsequently generates an image using two polarizers in a conventional manner. Both the SSCT and ZBD modes use higher voltages than the conventional TN mode, but are regarded as strong candidates for future bistable device applications. See also: Liquid Crystals: Overview; Calamitic Liquid Crystals; Nematic Liquid Crystals: Elastic Properties; Liquid Crystals, Molecular Design of : Calamitics Bibliography Alt P M, Pleshko P 1975 Scanning limitations of liquid crystal displays. IEEE Trans. Electron. De. 21, 146–55 Bahadur B (ed.) 1990 Liquid Crystals Applications and Uses. World Scientific, Singapore Berreman D W 1983 Numerical modelling of twisted nematic devices. In: Hilsum C, Raynes E P (eds.) Liquid Crystals: Their Physics, Chemistry and Applications. The Royal Society, London Bradshaw M J, Raynes E P, Fedak I, Leadbetter A J 1984 A correlation between short range smectic-like ordering and the elastic constants of nematic liquid crystals. J. Phys. 45, 157–62
Chandrasekhar S 1992 Liquid Crystals. Cambridge University Press, Cambridge de Gennes P G, Prost J 1993 The Physics of Liquid Crystals. Oxford University Press, Oxford Gooch C H, Tarry H A 1974 Optical characteristics of twisted nematic liquid crystal films. Electron. Lett. 10, 2–4 Heilmeier G H 1968 Dynamic scattering. Proc. IEEE 56, 1162–71 Raynes E P 1975 Optically active additives in twisted nematic devices. Re. Phys. Appl. 10, 117–20 Raynes E P 1998 Nematic and supertwisted nematic liquid crystal displays. In: Elston S J, Sambles J R (eds.) The Optics of Thermotropic Liquid Crystals. Taylor and Francis, London Schadt M, Helfrich W 1971 Voltage-dependent optical activity of a twisted nematic liquid crystal. Appl. Phys. Lett. 18, 127–8 Scheffer T J, Nehring J 1984 A new, highly multiplexable liquid crystal display. Appl. Phys. Lett. 45, 1021–3 Snell A J, Mackenzie K D, Spear W E, LeComber P G, Hughes A J 1981 Applications of amorphous Si FETs in addressable LCD panels. Appl. Phys. 24, 357–62 Waters C M, Brimmell V, Raynes E P 1983 Highly multiplexable dyed LCDs. Proc. 3rd Int. Display Res. Conf. Kobe, Japan
E. P. Raynes
Copyright ' 2001 Elsevier Science Ltd. All rights reserved. No part of this publication may be reproduced, stored in any retrieval system or transmitted in any form or by any means : electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without permission in writing from the publishers. Encyclopedia of Materials : Science and Technology ISBN: 0-08-0431526 pp. 6058–6065 7