Abstract
Thermal wave techniques can be used to excite thermal gradients within the volume to be evaluated and, hence, to achieve information on the interior of the sample under test.
The opportunities of thermal waves will be considered for the particular case of embedded piezoelectrics and the evaluation of their polarization state in construction elements, e.g., adaptronic structures. The described methods for this application are based on the pyroelectric effect whereas thermal excitation is induced by laser irradiation. Fundamentals of the pyroelectric effect are given and the resulting thermal problems are analyzed. Thermal methods recording the pyroelectric response both in the frequency (laser intensity modulation method including two- and three-dimensional polarization mapping) and in the time domains (thermal pulse method including thermal pulse tomography, thermal step method, thermal square wave method) are examined. Emphasis is given to the nonuniform resolution of thermal methods providing higher resolution in the near-surface region. Experimental pitfalls are highlighted. Nondestructive evaluation of piezoelectric transducers is illustrated by examples of lead zirconate titanate (PZT) plates embedded into low-temperature co-fired ceramics (LTCC), epoxy resins, thermoplastics, and die-casted aluminum.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adby PR (1980) Applied circuit theory: matrix and computer methods. Ellis Horwood series in electrical and electronic engineering. Ellis Horwood Ltd, London
Agnel S, Toureille A, Le Gressus C (1996) Study of the aging of impregnated paper of high power capacitors using the thermal step method and the thermally stimulated currents. Proceedings of conference on electrical insulation and dielectric phenomena – CEIDP ’96. https://doi.org/10.1109/CEIDP.1996.564656
Ahmed NH, Srinivas NN (1997) Review of space charge measurements in dielectrics. IEEE Trans Dielectr Electr Insul 4:644–656
Amjadi H (1996) Thermal-pulse investigation of thermally grown silicon dioxide electrets. In: 9th international symposium on electrets (ISE 9). https://doi.org/10.1109/ISE.1996.578079
Angström AJ (1863) XVII. New method of determining the thermal conductibility of bodies. Philos Mag Ser 4 25(166):130–142
Aryal S, Mellinger A (2013) Resolution-enhanced polarization imaging with focused thermal pulses. J Appl Phys 114:154109
Bauer S (1993) Method for the analysis of thermal-pulse data. Phys Rev B 47:11049–11055
Bauer S, Bauer-Gogonea S (2003) Current practice in space charge and polarization profile measurements using thermal techniques. IEEE Trans Dielectr Electr Insul 10:883–902
Bauer S, Ploss B (1988) Analysis of the spatial distribution of polarization in PVDF-foils from the frequency spectra of the pyroelectric current. In: Proceedings of 6th international symposium on electrets (ISE 6). https://doi.org/10.1109/ISE.1988.38519
Bauer S, Ploss B (1990) A method for the measurement of the thermal, dielectric, and pyroelectric properties of thin films and their applications for integrated heat sensors. J Appl Phys 68:6361–6367
Baumann T, Dacol F, Melcher RL (1983) Transmission thermal-wave microscopy with pyroelectric detection. Appl Phys Lett 43:71–73
Bezdetny NM, Zeinally AK, Khutorsky VE (1984) Investigation of the polarization distribution in ferroelectics by a dynamic pyro-effect method [in Russian]. Izv AN SSSR Ser Fiz 48:200–203
Biot MA (1970) Variational principles in heat transfer. Clarendon Press, Oxford
Blevin WR, Geist J (1974) Influence of black coatings on pyroelectric detectors. Appl Opt 13:1171–1178
Bloß P, DeReggi AS, Schäfer H (2000) Electric-field profile and thermal properties in substrate-supported dielectric films. Phys Rev B 62:8517–8530
Bosworth RCL (1946) Thermal inductance. Nature 158:309
Braccini M, Dupeux M (2012) Mechanics of solid interfaces. Wiley, Hoboken, chapter 8.3.1
Burfoot JC, Latham RV (1963) A new method for studying movements of electric domain walls. Br J Appl Phys 14:933–934
Cady WG (1964) Piezoelectricity, vol 2. Dover, New York, pp 699–711
Camia FM (1967) Traité de thermocinétique impulsionelle. Dunod, Paris
Carslaw HJ, Jaeger JC (1959) Conduction of heat in solids, 2nd edn. Oxford University Press, New York
Chen J, Zhang W, Feng Z, Cai W (2014) Determination of thermal contact conductance between thin metal sheets of battery tabs. Int J Heat Mass Transf 69:473–480
Chynoweth AG (1956) Dynamic method for measuring the pyroelectric effect with special reference to barium titanate. J Appl Phys 27:78–84
Clay W, Evans BJ, Latham RV (1974) A nondestructive pyroelectric display of an antiparallel polarization distribution in single-crystal barium titanate. J Phys D Appl Phys 7:1291–1295
Cole KS, Cole RH (1941) Dispersion and absorption in dielectrics I. Alternating current characteristics. J Chem Phys 9:341–351
Collins RE (1977) Measurement of charge distribution in electrets. Rev Sci Instrum 48:83–91
Cook WR, Berlincourt DA, Scholz FJ (1963) Thermal expansion and pyroelectricity in lead titanate zirconate and barium titanate. J Appl Phys 34:1392–1398
Coufal H, Grygier RK (1989) Charge profiles of thin electret films mapped with subnanosecond thermal pulses. J Opt Soc Am B6:2013–2017
Coufal HJ, Grygier RK, Horne DE, Fromm JE (1987) Pyroelectric calorimeter for photothermal studies of thin films and adsorbates. J Vac Sci Technol A 5:2875–2889
D’Azzo JJ, Houpis CH (1999) Nyquist, Bode and Nickols plots. In: Levine WS (ed) Control system fundamentals. CRC Press, Boca Raton, chapter 10.3
Dagher G, Holé S, Lewiner J (2006) A preliminary study of space charge distribution measurements at nanometer spatial resolution. IEEE Trans Dielectr Electr Insul 13:1036–1041
Davidson DW, Cole RH (1951) Dielectric relaxation in glycerol, propylene glycol, and n-propanol. J Chem Phys 19:1484–1490
Devonshire AF (1954) Theory of ferroelectrics. Adv Phys 3:85–130
Eydam E, Suchaneck G, Esslinger S, Schönecker A, Neumeister P, Gerlach G (2014) Polarization characterization of PZT disks and of embedded PZT plates by thermal wave methods. AIP Conf Proc 1627:31–36
Eydam A, Suchaneck G, Schwankl M, Gerlach G, Singer RF, Körner C (2015) Evaluation of polarisation state of light metal embedded piezoelectrics. Adv Appl Ceram 114:226–230
Eydam A, Suchaneck G, Gerlach G (2016a) Characterisation of the polarisation state of embedded piezoelectric transducers by thermal waves and thermal pulses. J Sensor Sensor Syst 5:165–170
Eydam A, Suchaneck G, Gerlach G (2016b) Non-destructive evaluation of integrated piezoelectric transducers by thermal waves and thermal pulses. Procedia Technol 26:59–65
Eydam A, Suchaneck G, Gerlach G (2016c) Thermal-pulse method for life monitoring of integrated piezoelectric transducers. Procedia Eng 168:848–851
Flössel M, Gebhardt S, Schönecker A, Michaelis A (2010) Development of a novel sensor-actuator-module with ceramic multilayer technology. J Ceram Sci Technol 1:55–58
Gaudenzi P (2009) Smart structures: physical behaviour, mathematical modelling and applications. Wiley, Chichester
Gerlach G, Shvedov D, Norkus V (2004) Packaging influence on acceleration sensitivity of pyroelectric infrared detectors. In: Proceedings of sixth IEEE CPMT conference on high density microsystem design and packaging and component failure analysis, HDP’04. https://doi.org/10.1109/HPD.2004.1346715
Gerlach G, Suchaneck G, Movchikova A, Malyshkina OA (2007) Nondestructive testing of ferroelectrics by thermal wave methods. Proc SPIE 6530:65300B. https://doi.org/10.1117/12.715534
Glass AM (1968) Dielectric, thermal, and pyroelectric properties of ferroelectric LiTaO3. Phys Rev 172:564–571
Göber H, Erk S, Grigull U (1955) Die Grundgesetze der Wärmeübertragung. Springer, Berlin, p 82
Groetsch CW (2007) Integral equations of the first kind, inverse problems and regularization: a crash course. J Phys Conf Ser 73:012001
Hadni A, Thomas R (1972) Laser study of reversible nucleation sites in triglycine sulphate and applications to pyroelectric detectors. Ferroelectrics 4:39–49
Hadni A, Henninger Y, Thomas R, Vergnat P, Bruno Wyncke B (1965) Sur les propriétés pyroélectriques de quelques matériaux et leur application à la détection de l’infrarouge. J Phys France 26:345–360
Hadni A, Thomas R, Perrin J (1969) Response of a triglycine sulphate pyroelectric detector to high frequencies (300 kHz). J Appl Phys 40:2740–2745
Havriliak S, Negami S (1967) A complex plane representation of dielectric and mechanical relaxation processes in some polymers. Polymer 8:161–210
Holé S (2008) Resolution of direct space charge distribution measurement methods. IEEE Trans Dielectr Electr Insul 15:861–871
Hufenbach W, Gude M, Modler N, Heber T, Winkler A, Weber T (2013) Process chain modelling and analysis for the high-volume production of thermoplastic composites with embedded piezoceramic modules. Smart Mater Res 2013:201631
Imburgia I, Romano P, Caruso M, Viola F, Miceli R, Riva Sanseverino E, Madonia A, Schettino G (2016) Contributed review: review of thermal methods for space charge measurement. Rev Sci Instrum 87:111501
Kepler RG, Anderson RA (1978) Piezoelectricity and pyroelectricity in polyvinylidene fluoride. J Appl Phys 49:4490–4494
Kremer F, Schoenhals A (eds) (2003) Broadband dielectric spectroscopy. Springer, Berlin, pp 62–72
Landau LD, Lifshitz EM (1969) Mechanics (Volume 1 of a course of theoretical physics). Pergamon Press, Oxford, p 59
Lang SB (1990) New theoretical analysis for the laser intensity modulation method (LIMM). Ferroelectrics 106:269–274
Lang SB (1991) Laser intensity modulation method (LIMM): experimental techniques, theory and solution of the integral equation. Ferroelectrics 118:343–361
Lang SB (1998) An analysis of the integral equation of the surface laser intensity modulation method using the constrained regularization method. IEEE Trans Dielectr Electr Insul 5:70–76
Lang SB (2004) Laser intensity modulation method (LIMM): review of the fundamentals and a new method for data analysis. IEEE Trans Dielectr Electr Insul 11:3–12
Lang SB (2006) Fredholm integral equation of the laser intensity modulation method (LIMM): solution with the polynomial regularization and L-curve methods. J Mater Sci 41:147–153
Lang SB, Das-Gupta DK (1986) Laser-intensity-modulation method: a technique for determination of spatial distributions of polarization and space charge in polymer electrets. J Appl Phys 59:2151–2160
Lang SB, Fleming R (2009) A comparison of three techniques for solving the Fredholm integral equation of the laser intensity modulation method (LIMM). IEEE Trans Dielectr Electr Insul 16:809–814
Lang SB, Rosenman G, Rushin S, Kugel V, Nir D (1992) Electron emission and spontaneous polarization distribution of proton-exchanged LiNbO3. Ferroelectrics 133:253–258
Leal Ferreira GF (1989) On the deconvolution of heat-pulse like signals. J Appl Phys 66:4924–4927
Lines ME, Glass AM (1977) Principles and application of ferroelectrics and related materials. Clarendon Press, Oxford, chapter 5.2
Liu ST, Zook JD (1974) Evaluation of Curie constants of ferroelectric crystals from pyroelectric response. Ferroelectrics 7:171–173
Liu S, Grinberg I, Rappe AM (2013) Exploration of the intrinsic inertial response of ferroelectric domain walls via molecular dynamics simulations. Appl Phys Lett 103:232907
Mah JW, Shanmugan S, Mutharasu D (2017) Impact of temperature, pressure, and current on thermal resistance of thermal interface material in optoelectronics device. J Optoelectron Biomed Mater 9:79–84
Malyshkina OV, Movchikova AA, Suchaneck G (2007) New method for the determination of the pyroelectric current spatial distribution in ferroelectric materials [in Russian]. Phys Solid State 49:2144–2147 [Fiz Tverd Tela 49:2045–2048]
Malyshkina OV, Movchikova AA, Grechishkin RM, Kalugina ON (2010) Use of the thermal square-wave method to analyze polarization state in ferroelectric materials. Ferroelectrics 400:63–75
Mandelis A, Zver MM (1985) Theory of photopyroelectric spectroscopy of solids. J Appl Phys 57:4421–4430
Mandelis A, Nicolaides L, Yan C (2001) Structure and the reflectionless/refractionless nature of parabolic diffusion-wave fields. Phys Rev Lett 87:020801
Mellinger A (2004) Unbiased iterative reconstruction of polarization and space charge profiles from thermal-wave experiments. Meas Sci Technol 15:1347–1353
Mellinger A, Singh R, Gerhard-Multhaupt R (2005a) Fast thermal-pulse measurements of space-charge distributions in electret polymers. Rev Sci Instrum 76:013903
Mellinger A, Singh R, Wegener M, Wirges W, Gerhard-Multhaupt R, Lang SB (2005b) Three-dimensional mapping of polarization profiles with thermal pulses. Appl Phys Lett 86:082903
Mellinger A, Flores-Suárez R, Wegener M, Wirges W, Gerhard-Multhaupt R, Singh R (2006) Thermal-pulse tomography of polarization distributions in a cylindrical geometry. IEEE Trans Dielectr Electr Insul 13:1030–1035
Mopsik FI, DeReggi AS (1982) Numerical evaluation on the dielectric polarization distribution from thermal pulse data. J Appl Phys 53:4333–4339
Movchikova A, Malyshkina OV, Pedko BB, Suchaneck G, Gerlach G (2008a) Polarization profiling of ferroelectrics by thermal square wave methods. Ferroelectrics 367:38–44
Movchikova A, Malyshkina O, Suchaneck G, Gerlach G, Steinhausen R, Langhammer HT, Pientschke C, Beige H (2008b) Study of the pyroelectric behavior of BaTi1-xSnxO3 piezo-ceramics. J Electroceram 20:43–46
Movchikova A, Malyshkina OV, Pedko BB, Suchaneck G, Gerlach G (2009) The influence of doping on the pyroelectric response of SBN single crystals. Ferroelectrics 378:186–194
Movchikova A, Suchaneck G, Malyshkina OV, Pedko BB, Gerlach G (2010) Thermal wave study of piezoelectric coefficient distribution in PMN-PT single crystals. Adv Appl Ceram 109:131–134
Neugschwandtner GS, Schwödiauer R, Bauer-Gogonea S, Bauer S (2001) Piezo- and pyroelectricity of a polymer-foam space-charge electret. J Appl Phys 89:4503–4511
Notingher P, Agnel S, Fruchier O, Toureille A, Rousset B, Sanchez JL (2004) On the use of the thermal step method as a tool for characterizing thin layers and structures for micro and nano-electronics. J Optoelectron Adv Mater 6:1089–1906
Notingher P, Holé S, Baudon S, Fuchier O, Boyer L, Agnel S (2012) Toward non-destructive high resolution thermal methods for electric charge measurements in solid dielectrics and components. In: ESA2012- electrostatics joint conference, Cambridge, June 2012. Online publication. http://www.electrostatics.org/images/ESA2012_M3.pdf. Accessed 24 Nov 2017
Nye JF (1995) Physical properties of crystals: their representation by tensors and matrices. Clarendon Press, Oxford, chapter 10.4.4
Parker WJ, Jenkins RJ, Butler CP, Abbott GL (1961) Flash method of determining thermal diffusivity, heat capacity, and thermal conductivity. J Appl Phys 32:1679–1684
Perrin B, Bonello B, Jeannet J-C, Romatet E (1996) Interferometric detection of hypersound waves in modulated structures. Prog Nat Sci 6:444–448
Perry CH, Khan BN, Rupprecht G (1964) Infrared studies of perovskite titanates. Phys Rev 135:A408–A412
Peterson RL, Day GW, Gruzensky PM, Phelan RJ (1974) Analysis of response of pyroelectric optical detector. J Appl Phys 45:3296–3303
Petre A, Marty-Dessus D, Berquez L, Franceschi JL (2006) Space charge cartography by FLIMM on SEM-irradiated PTFE thin films. J Electrost 64:492–497
Petzelt J, Nuzhnyy D, Bovtun V, Kempa M, Savinov M, Kamba S, Hlinka J (2015) Lattice dynamics and dielectric spectroscopy of BZT and NBT lead-free perovskite relaxors – comparison with lead-based relaxors. Phase Transit 88:320–332
PI Ceramic GmbH (2017) Piezoelectric ceramic products: fundamentals, characteristics and applications. https://www.piceramic.com/en/products/piezoceramic-materials/#c15193. Accessed 24 Nov 2017
Ploss B, Bianzano O (1994) Polarization profiling of the surface region of PVDF and P(VDF-TrFE).In: IEEE 8th international symposium on electrets. https://doi.org/10.1109/ISE.1994.514769
Ploss B, Emmerich R, Bauer S (1992) Thermal wave probing of pyroelectric distributions in the surface region of ferroelectric materials: a new method of analysis. J Appl Phys 72:5363–5370
Prudnikov AP, Brychkov YA, Marichev OI (1992) Integrals and series, vol. 1: Elementary functions. Taylor & Francis, London, p 730
Putley EH (1970) The pyroelectric detector. In: Willardson RK, Beer AC (eds) Semiconductors and semimetals, vol 5. Academic, New York, pp 259–285
Qiu X, Hollander L, Flores Suarez R, Wirges W, Gerhard R (2010) Polarization from dielectric-barrier discharges in ferroelectrets: mapping of the electric-field profiles by means of thermal-pulse tomography. Appl Phys Lett 97:072905
Raffmetal (2017) EN 46000 data sheet. www.raffmetal.com/scarica_file.asp?c=/dati/SearchAlloy/ENG/&f=EN46000.pdf. Accessed 24 Nov 2017
Reboul JM (2011) Thermal waves interferences for space charge measurements in dielectrics. In: 14th international symposium on electrets (ISE). https://doi.org/10.1109/ISE.2011.6084983
Reboul JM, Mady F (2004) Space charge measurements by the alternating thermal wave method: thermal analysis and simulations for data processing improvement. In: Proceedings of the 2004 I.E. international conference on solid dielectrics ICSD. https://doi.org/10.1109/ICSD.2004.1350339
Reboul JM, Cherifi A, Carin R (2001) A new method for space charge measurements in dielectric films for power capacitors. IEEE Trans Dielectr Electr Insul 8:753–759
Rose A (1973) Vision – human and electronic. Plenum Press, New York
Rübner M, Körner C, Singer RF (2008) Integration of piezoceramic modules into die castings – procedure and functionalities. Adv Sci Technol 56:170–175
Sakai S, Date M, Furukawa T (2002) Development of polarization distribution in fatigued films of ferroelectric vinylidene fluoride/trifluoroethylene copolymer. Jpn J Appl Phys 41:3822–3828
Salazar A (2006) Energy propagation of thermal waves. Eur J Phys 27:1349–1355
Samoilov VB, Yoon YS (1998) Frequency response of multilayer pyroelectric sensors. IEEE Trans Ultrason Ferroelectr Freq Control 45:1246–1254
Sandner T (2003) Verfahren zur tiefenaufgelösten Polarisationsbestimmung von pyroelektrischen PZT-Dünnschichten für IR-Sensoren. w.e.b.-Universitätsverlag, Dresden
Sandner T, Suchaneck G, Koehler R, Suchaneck A, Gerlach G (2002) High frequency LIMM – a powerful tool for ferroelectric thin film characterization. Integr Ferroelectr 46:243–257
Schein LB, Cressman PJ, Cross LE (1978) Electrostatic measurements of tertiary pyroelectricity in partially clamped LiNbO3. Ferroelectrics 22:945–948
Sea Ceramics Technology (2017a) Thermal properties of ceramics and metal/metal composites. http://seaceramics.com/Download/Reference%20Data/Cer-Metal%20thermal%20properties.pdf. Accessed 24 Nov 2017
Sea Ceramics Technology (2017b) Table of LTCC materials properties. http://seaceramics.com/Download/Reference%20Data/LTCC%20PROPERTY2.pdf. Accessed 24 Nov 2017
Sessler GM (1997) Charge distribution and transport in polymers. IEEE Trans Dielectr Electr Insul 4:614–628
Stewart M, Cain M (2008) Spatial characterization of piezoelectric materials using the scanning laser intensity modulation method (LIMM). J Am Ceram Soc 91:2176–2181
Suchaneck G, Lin W-M, Koehler R, Sandner T, Gerlach G, Krawietz R, Pompe W, Deineka A, Jastrabik L (2002) Characterization of RF-sputtered self-polarized PZT thin films for IR sensor arrays. Vacuum 66:473–478
Suchaneck G, Hu W, Gerlach G, Flössel M, Gebhardt S, Schönecker A (2011) Nondestructive evaluation of polarization in LTCC/PZT piezoelectric modules by thermal wave methods. Ferroelectrics 420:25–29
Suchaneck G, Eydam A, Hu W, Kranz B, Drossel W-G, Gerlach G (2012) Evaluation of polarization of embedded piezoelectrics by the thermal wave method. IEEE Trans Ultrason Ferroel Freq Control 59:1950–1954
Suchaneck G, Eydam A, Rübner R, Schwankl M, Gerlach G (2013a) A simple thermal wave method for the evaluation of the polarization state of embedded piezoceramics. Ceram Int 39-S1:S587–S590
Suchaneck G, Eydam A, Gerlach G (2013b) A laser intensity modulation method for the evaluation of the polarization state of embedded piezoceramics. Ferroelectrics 453:127–132
Toureille A, Reboul JP (1988) The thermal-step-technique applied to the study of charge decay in polyethylene thermoelectrets. In: IEEE 6th international symposium on electrets (ISE 6). https://doi.org/10.1109/ISE.1988.38518
Tuncer E, Lang SB (2006) Kramers-Kronig relations in laser intensity modulation method. Phys Rev B 74:113109
van der Ziel A (1973) Pyroelectric response and D* of thin pyroelectric films on a substrate. J Appl Phys 44:546–549
Voigt W (1910) Lehrbuch der Kristallphysik. Teubner, Leipzig
von Laue M (1925) Piezoelektrisch erzwungene Schwingungen von Quarzstäben. Z Phys 34:347–361
von Seggern H (1978) Thermal-pulse technique for determining charge distributions: effect of measurement accuracy. Appl Phys Lett 33:134–137
von Seggern H, West JE, Kubli RA (1984) Determination of charge centroids in two-side metallized electrets. Rev Sci Instrum 55:964967
Wilkie WK, Bryant GR, High JW. Fox RL, Hellbaum RF, Jalink A, Little BD, Mirick PH (2000) Low-cost piezocomposite actuator for structural control applications. In: Proceedings of SPIE 3991, smart structures and materials 2000: industrial and commercial applications of smart structures technologies. https://doi.org/10.1117/12.388175
Wu Q, Zhang X-C (1995) Free-space electro-optic sampling of terahertz beams. Appl Phys Lett 67:3523–3525
Xu-Sheng W (1993) Tertiary pyroelectric effect on thick ferroelectric crystal plates with partially uniform heating. Ferroelectr Lett Sect 15:159–165
Yilmaz S, Bauer S, Wirges W, Gerhard-Multhaupt R (1993) Scanning electro-optical and pyroelectrical microscopy for the investigation of polarization patterns in poled polymers. Appl Phys Lett 63:1724–1726
Zajosz J (1979) Pyroelectric response to step radiation signals in thin ferroelectric films on a substrate. Thin Solid Films 62:229–236
Zheng F, Zhang Y, An Z, Liu C, Dong J, Lin C (2013) Thermal pulse method with an applied field. In: IEEE international conference on solid dielectrics (ICSD). https://doi.org/10.1109/ICSD.2013.6619841
Zook JD, Liu ST (1978) Pyroelectric effect in thin film. J Appl Phys 49:4604–4606
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this entry
Cite this entry
Suchaneck, G., Eydam, A., Gerlach, G. (2019). Thermal Wave Techniques. In: Ida, N., Meyendorf, N. (eds) Handbook of Advanced Nondestructive Evaluation. Springer, Cham. https://doi.org/10.1007/978-3-319-26553-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-26553-7_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26552-0
Online ISBN: 978-3-319-26553-7
eBook Packages: EngineeringReference Module Computer Science and Engineering