For an opaque solid, the fraction of incident radiation absorbed is
$$P\left\{ {{X_j} = e} \right\} = \frac{1} {{2d'}}\;\;\left| e \right| = 1$$
where e is the emissivity and R 0 is the reflectivity at normal incidence. R 0 and ∈ can be calculated from measurements of optical constants or the complex refractive index. For a complex refractive index,
$$ m = n - ik $$
the reflectivity at normal incidence is
$$ {R_{0}}\frac{{{{(n - 1)}^{2}} + {k^{2}}}}{{{{(n + 1)}^{2}} + {k^{2}}}}$$
The emissivity is then
$$ \in = \frac{{4n}}{{{{(n + 1)}^{2}} + {k^{2}}}} $$


Laser Power Welding Speed Laser Welding Heat Affect Zone Laser Heating 


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  1. H. J. Allelein, R. Hecker, A. Max, Th. Overhoff, and D. Stover (1979), J. Appl. Phys.50, 6162.Google Scholar
  2. T. R. Anthony and H. E. Cline (1977),J. Appl. Phys.48, 3888.Google Scholar
  3. T. R. Anthony and H. E. Cline (1978),J. Appl. Phys.49, 1248.Google Scholar
  4. M. I. Arzuov, A. I. Barchukov, F. V. Bunkin, V. I. Kunov, and A. M. Prokhorov (1975), Sov. J. Quantum Electron.5, 523.Google Scholar
  5. M. I. Arzuov, M. E. Karasev, V. I. Konov, V. V. Kostin, S. M. Metev, A. S. Silenok, and N. I. Chapliev (1979), Sov. J. Quantum Electron.8, 892.Google Scholar
  6. J. F. Asmus (1979), Chem. Abstr.90, 38086.Google Scholar
  7. V. P. Babenko and V. P. Tychinskh (1973), Sov. J. Quantum Electron.2, 399.Google Scholar
  8. J. M. Baldwin (1970), Appl. Spectrosc.24, 429.Google Scholar
  9. J. M. Baldwin (1973),J. Appl. Phys.44, 3362.Google Scholar
  10. W. C. Ball and C. M. Banas (1974), Soc. Auto. Eng., Report 740863.Google Scholar
  11. C. M. Banas, A. P. Walch, and C. O. Brown (1971), Recordings of the 11th Symposium on Electron Ion, Laser Beam Technology, IEEE, San Francisco Press, San Francisco.Google Scholar
  12. V. Baranauskas, C. I. Z. Mammana, R. E. Klinger, and J. E. Greene (1980), Appl. Phys.36, 930.Google Scholar
  13. B. T. Barnes (1966),J. Opt. Soc. Am.56, 1546.Google Scholar
  14. S. M. Bedair and H. P. Smith (1969),J. Appl. Phys.40, 4776.Google Scholar
  15. A. L. Berg, D. E. Lood (1968), Solid State Electron.11, 773.Google Scholar
  16. I. M. Beterov, V. P. Chebotaev, N. I. Yurshina, and B. Ya Yurshin (1978), Sov. J. Quantum Electron.8, 1310.Google Scholar
  17. V. M. Boyakov, V. M. Epikhin, B. A. Kalin, M. K. Maklatov, I. N. Mikolaev, and G. N. Shishkin (1978), Sov. J. Quantum Electron.8, 902.Google Scholar
  18. L. Braun and D. Breuer (1969), Solid State Technol.12, 56.Google Scholar
  19. E. M. Breinan and C. M. Banas (1981), in Advances in Metal Processing J. J. Burke, R. Mehrabian, and V. Weiss, Eds., Plenum Press, New York.Google Scholar
  20. E. M. Breinan, C. M. Banas, and M. A. Greenfield (1975), United Technol. Res. Ctr. Report R75–111 087–3.Google Scholar
  21. E. M. Breinan, B. H. Kear, and C. M. Banas (1976), Phys. Today, November, p. 44.Google Scholar
  22. A. D. Brisbane and T. M. Jackson (1968), Electron. Compon.9, 73.Google Scholar
  23. K. Brugger (1972), J. Appl. Phys.53, 577.Google Scholar
  24. K. R. Bube (1975), Am. Ceram. Soc. Bull.54, 528.Google Scholar
  25. L. Buene, J. M. Poate, D. C. Jacobson, C. W. Draper, and J. K. Hirvonen (1980), Appl. Phys. Lett.37, 385.Google Scholar
  26. L. L. Burns (1980), Laser Focus, July, p. 48.Google Scholar
  27. C. A. Burrus and L. A. Goldren (1977), Appl. Phys. Lett.31, 383.Google Scholar
  28. C. Cali, V. Danen, A. Orioli, and R. Riva-Sanseverino (1976), Appl. Opt.15, 1327.Google Scholar
  29. D. K. Campbell and D. W. Sweeney (1978), Appl. Opt.17, 3727.Google Scholar
  30. C. O. Carlson, E. Stone, H. L. Bernstein, W. K. Tomita, and W. C. Myers (1966), Science154, 1550.Google Scholar
  31. H. S. Carslaw and J. C. Jaeger (1959), Conduction of Heat in Solids, 2nd ed., Oxford University Press (Clarendon), London and New York.Google Scholar
  32. D. Chen and J. D. Zook(1975), Proc. IEEE63, 1207.Google Scholar
  33. D. Chen, B. Koepke, J. D. Zook, and E. Bernal. (1976), Appl. Phys. Lett.29, 657.Google Scholar
  34. C. P. Christensen and K. M. Lakin (1978), Appl. Phys. Lett.32, 254.Google Scholar
  35. J. Clarke and W. M. Steen (1979), Proceedings of the Laser ’79 Conference, Munich.Google Scholar
  36. H. E. Cline and T. R. Anthony (1977),J. Appl. Phys. 48, 3895.Google Scholar
  37. B. Cockayne and D. B. Gasson (1971),J. Mater. Sci.6, 126.Google Scholar
  38. M. I. Cohen (1972) in Laser Handbook, F. T. Arecchi and E. O. Schulz-Dubois, Eds., North Holland, Amsterdam, p. 1577.Google Scholar
  39. M. I. Cohen and J. P. Epperson (1968a), Adv. Electron. Electron Phys. Suppl.4, 139.Google Scholar
  40. M. I. Cohen and J. P. Epperson (1968b), in Electron Beam and Laser Beam Technology, L. Marton and A. B. El-Kareh, Eds., Academic Press, New York.Google Scholar
  41. M. I. Cohen, B. A. Unger, and J. F. Milkowsky (1968), Bell Syst. Tech. J.47, 385.Google Scholar
  42. S. M. Copley, D. Beck, O. Esquivel, and M. Bass (1979), in Laser Solid Interactions and Laser Processing, S. D. Ferris et al., Eds., AIP Conference Proceedings, 3, American Institute of Physics, New York.Google Scholar
  43. C. Courtney and W. M. Steen (1978), Proceedings of Advances in Surface Coating Technology, London, p. 219.Google Scholar
  44. R. C. Crafer (1976), Weld. Inst. Res. Bull.17, 28.Google Scholar
  45. F. W. Dabby and U. C. Paek (1972), IEEE J. Quantum Electron.QE-8, 106.Google Scholar
  46. K. Daree and W. Kaiser (1978), Opt. Laser Technol., April, p. 65.Google Scholar
  47. T. F. Deutsch, D. J. Ehrlich, and R. M. Osgood (1979), Appl. Phys. Lett.35, 175.Google Scholar
  48. W. W. Duley (1976), CO2Lasers: Effects and Applications, Academic Press, New York.Google Scholar
  49. W. W. Duley and J. N. Gonsalves (1974), Opt. Laser Technol.6, 78.Google Scholar
  50. W. W. Duley, D. J. Semple, J.-P. Morency, and M. Gravel (1979), Opt. Laser Technol.11, 281.Google Scholar
  51. M. Eboo, W. M. Steen, and J. Clarke (1978), Advances in Welding, Proceedings, Harrogate.Google Scholar
  52. K. Egashira and M. Kobayashi (1977a), Appl. Opt.16, 1636.Google Scholar
  53. K. Egashira and M. Kobayashi (1977b), Appl. Opt.16, 2743.Google Scholar
  54. D. J. Ehrich, R. M. Osgood, and T. F. Deutsch (1980), Appl. Phys. Lett.36, 916.Google Scholar
  55. K. Eickhoff and K. Gürs (1969),J. Crystal Growth6, 21.Google Scholar
  56. W. A. Elliott, F. P. Gagliano and G. Krauss (1973), Met. Trans.4, 2031.Google Scholar
  57. S. L. Engel (1976), Am. Mach. May, p. 107.Google Scholar
  58. S. L. Engel (1976), Laser Focus, February, p. 44.Google Scholar
  59. S. L. Engel (1978), Laser Focus, December, p. 66.Google Scholar
  60. A. Engel, J. Steffen and G. Herziger (1974), Appl. Opt.13, 269.Google Scholar
  61. J. P. Epperson, R. W. Dyer, and J. C. Grzywa (1966), West Elec. Eng.10, 2.Google Scholar
  62. N. N. Evtikhiev, G. R. Levinson, K. P. Tsvetaev, and O. V. Golosnoi (1974), Sov. J. Quantum Electron.4, 527.Google Scholar
  63. M. L. Faber (1974), IEEE Trans. Parts. Hybrids, Packag.10, 169.Google Scholar
  64. J. A. Fox (1975), Appl. Phys. Lett.26, 682.Google Scholar
  65. H. Fujita, Y. Suzaki, and A. Tachibana (1976), Appl. Opt.15, 230.Google Scholar
  66. F. P. Gagliano, R. M. Lumley, and L. S. Watkins (1969), Proc. IEEE57, 114.Google Scholar
  67. F. P. Gagliano and V. J. Zaleckas (1972), in Lasers in Industry, S. S. Charschan, Ed., P. 139, Van Nostrand Reinhold, Princeton.Google Scholar
  68. D. B. Gasson and B. Cockayne (1970),J. Mater. Sci.5, 100.Google Scholar
  69. D. S. Gnanamuthu, C. B. Shaw, W. E. Lawrence, and M. R. Mitchell (1979), in Laser Solid Interactions and Laser Processing—1978, S. D. Ferris et al., Eds., AIP Conference Proceedings, Vol. 50, American Institute of Physics, New York, p. 173.Google Scholar
  70. E. E. Gray (1972), IEEE Trans. Magn.MAG-8, 416.Google Scholar
  71. L. E. Greenwald, E. M. Breinan, and B. H. Kear (1979), in Laser Solid Interactions and Laser Processing, S. D. Ferris et al., Eds., AIP Conference Proceedings, Vol. 50, American Institute of Physics, New York, p. 189.Google Scholar
  72. D. C. Hamilton and D. J. James (1976),J. Phys. D9, L41.Google Scholar
  73. D. C. Hamilton and I. R. Pashby (1979), Opt. Laser Technol., August, p. 183.Google Scholar
  74. M. Hanabusa, A. Namiki, and K. Yoshihara (1979), Appl. Phys. Lett.35, 626.Google Scholar
  75. J. E. Harry and F. W. Lunau (1972), IEEE Trans. Ind. Appl.IA-8, 418.Google Scholar
  76. G. Hass and J. B. Ramsey (1969), Appl. Opt.8, 1115.Google Scholar
  77. R. C. Headley (1973), Electron.46, 121.Google Scholar
  78. J. W. Hill, M. J. Lee, I. J. Spalding (1974), Opt. Laser Technol., December, p. 276.Google Scholar
  79. G. Holzinger, K. Kosanke, and W. Menz (1973), Opt. Laser Technol., December, p. 257.Google Scholar
  80. E. Inoue, H. Kokado, I. Shimizu, and S. Ootsuka (1973), Photogr. Sci. Eng.17, 405.Google Scholar
  81. R. E. Jaeger (1976), Am. Ceram. Soc. Bull.55, 270.Google Scholar
  82. R. E. Jaeger and W. Logan (1973), Opt. Spectra, November, p. 40.Google Scholar
  83. A. Kestenbaum (1979), J. Appl. Phys.50, 5012.Google Scholar
  84. P. H. Kim, K. Taki, and S. Namba (1971), Recordings of the 11th Symposium on Electron, Ion, Laser Beam Technology, IEEE, San Francisco Press, San Francisco, p. 375.Google Scholar
  85. Y-W Kim, P. R. Strutt, and H. Nowotny (1979), Met. Trans.10A, 881.Google Scholar
  86. K. Kinoshita and K. Egashira (1978), Appl. Opt.17, 1210.Google Scholar
  87. J. K. Kliwer (1973), J. Appl. Phys.44, 490.Google Scholar
  88. F. Kummer and I. Taitl (1977), Chem. Abstr.89, 98291.Google Scholar
  89. V. I. Little, P. Y. Key, R. Wiltscher, and D. M. Rowley (1971), Nature, Phys. Sci.232, 165.Google Scholar
  90. E. V. Locke and R. A. Hella (1974), IEEE J. Quantum ElectronQE-10, 179.Google Scholar
  91. E. V. Locke, E. D. Hoag, and R. A. Hella (1972), IEEE J. Quantum Electron.QE-8, 132.Google Scholar
  92. J. Longfellow (1970). Rev. Sci. Instrum.41, 1485.Google Scholar
  93. J. Longfellow (1971), Am. Ceram. Soc. Bull.50, 251.Google Scholar
  94. D. Y. Lou (1977), J. Appl. Phys.48, 2015.Google Scholar
  95. R. M. Lumley (1969), Am. Ceram. Soc. Bull48, 850.Google Scholar
  96. F. W. Lunau (1970), Conference on Electronic Methods of Machining, Forming, and Coating (reprint).Google Scholar
  97. H. Lydtin (1972), 3rd International Conference on Chemical Vapor Deposition, Salt Lake City, April 24.Google Scholar
  98. M. E. Maher and R. B. Hall (1978), J. Appl. Phys.49, 2254.Google Scholar
  99. S. Marcus, J. E. Lowder and D. L. Mooney (1976),J. Appl. Phys.47, 2966.Google Scholar
  100. A. J. Martin, R. H. Buck, R. G. Loasby, and J. Savage (1968), Thin Solid Films2, 253.Google Scholar
  101. D. Maydan (1971), Bell Syst. Tech. J.50, 1761.Google Scholar
  102. J. Mazumder (1977), Ph.D. thesis, University of London.Google Scholar
  103. J. Mazumder and W. M. Steen (1977), Proceedings of the Laser 17 Conference, Munich, p. 307.Google Scholar
  104. J. Mazumder and W. M. Steen (1980), J. Appl. Phys.51, 941.Google Scholar
  105. J. A. McKay and J. T. Schriempf (1979), Appl. Phys. Lett.35, 433.Google Scholar
  106. R. Mehrabian, S. Kou, S. C. Hsu, and M. Munitz (1979), AIP Conf. Proc.50, 129.Google Scholar
  107. C. H. Miller and T. A. Osial (1969), Status Report on 250-W CO2 Laser for Applications in the Pulp and Paper Industry, IEEE 1969, Annual Pulp Paper Industry Technical Conference, Atlanta.Google Scholar
  108. C. J. Mohr, J. A. Ring, E. H. Stevens, and R. A. Baker (1977), Proc. IEEE65, 269.Google Scholar
  109. P. Moore, C. Kim, and L. S. Weinman (1979), AIP Conf. Proc.50, 221.Google Scholar
  110. A. J. Moorhead (1971), Weld. J.50, 97.Google Scholar
  111. J. M. Moran (1971), Appl. Opt.10, 412.Google Scholar
  112. M. Mori and H. Kumehara (1976), Annal. CIRP25, 115.Google Scholar
  113. Y. Nakada and M. A. Giles (1971),J. Am. Ceram. Soc.54, 354.Google Scholar
  114. S. L. Narasimhau, S. M. Copley, E. W. van Stryland, and M. Bass (1979), Met. Trans.10A, 654.Google Scholar
  115. G. Nath (1974), Opt. Laser Technol., October, p. 233.Google Scholar
  116. L. S. Nelson and N. L. Richardson (1972), Mater. Res. Bull.7, 971.Google Scholar
  117. L. S. Nelson, N. L. Richardson, K. Keil, and S. R. Skaggs (1973), High Temp. Sci.5, 138.Google Scholar
  118. L. S. Nelson, S. R. Skaggs, and N. L. Richardson (1970), J. Am. Ceram. Soc. Bull.53,113.Google Scholar
  119. L. S. Nelson, A. G. Whittaker, and B. Tooper (1972), High Temp. Sci.4, 445.Google Scholar
  120. J. C. North (1977), J. Appl. Phys.48, 2419.Google Scholar
  121. M. Oakes (1978), Opt. Eng.17, 217.Google Scholar
  122. U. C. Paek (1974), Appl. Opt.13, 1383.Google Scholar
  123. U. C. Paek and A. Kestenbaum (1973),J. Appl. Phys.44, 2260.Google Scholar
  124. U. C. Paek and A. L. Weaver (1975), Appl. Opt.14, 294.Google Scholar
  125. T. G. Pavlopoulos and K. Crabtree (1974),J. Appl. Phys.45, 4964.Google Scholar
  126. J. F. Ready (1971), Effects of High Power Laser Radiation, Academic Press, New York.Google Scholar
  127. J. F. Ready (1978), Industrial Applications of Lasers, Academic Press, New York.Google Scholar
  128. J. E. Robin (1978), J. Appl. Phys.49, 5306.Google Scholar
  129. J. E. Robin and P. Nordin (1975a), Appl. Phys. Lett.26, 289.Google Scholar
  130. J. E. Robin and P. Nordin (1975b), Appl. Phys. Lett.27, 593.Google Scholar
  131. J. E. Robin and P. Nordin (1976), Appl. Phys. Lett.29, 3.Google Scholar
  132. D. M. Roessler and V. G. Gregson (1978), Appl. Opt.17, 992.Google Scholar
  133. H. Schonhorn, C. R. Kurkjian, R. E. Jaeger, H. N. Vazirani, R. V. Albarino, and F. V. Di Marcello (1976), Appl. Phys. Lett.29, 712.Google Scholar
  134. H. Schonhorn, H. N. Vazirani, and H. L. Frisch (1978), J. Appl. Phys.49, 3703.Google Scholar
  135. H. Schwarz and H. A. Tourtellote (1969), J. Vac. Sci. Technol.6, 373.Google Scholar
  136. F. Schwirzke, H. Brinkschulte, and M. Hashmi (1974), J. Appl. Phys.46, 4891.Google Scholar
  137. F. Schwirzke, L. Oren, S. Talmadge, and R. J. Taylor (1978), Phys. Rev. Lett.40, 1181.Google Scholar
  138. J. G. Scigman (1968), Microelectron. Reliability7, 305.Google Scholar
  139. J. G. Scigman (1969), Microelectron. Reliability8, 87.Google Scholar
  140. J. Shewell (1977), Weld. Des. Fab., June, p. 100.Google Scholar
  141. I. P. Shkarofsky (1975), RCA Rev.36, 336.Google Scholar
  142. S. H. Slivinsky and N. E. Ogle (1977), J. Appl. Phys.48, 3660.Google Scholar
  143. H. M. Smith and A. F. Turner (1965), Appl. Opt.4, 147.Google Scholar
  144. M. Sparks (1976), J. Appl. Phys.47, 837.Google Scholar
  145. V. M. Steen (1977), Lett. Heat Mass Trans.4, 167.Google Scholar
  146. W. M. Steen (1978), Advances in Surface Coating Technology International Conference, London, p. 175.Google Scholar
  147. W. M. Steen (1979), private communication.Google Scholar
  148. W. M. Steen and M. Eboo (1979), Met. Const.11, 332.Google Scholar
  149. F. Stern (1973), J. Appl. Phys.44, 4204.Google Scholar
  150. B. Steverding, R. W. Conrad, and H. P. Dudel (1979),J. Appl. Phys.50, 6713.Google Scholar
  151. P. R. Strutt, D. A. Gilbert, H. Nowotny, and Y-M Kim (1979), in Laser Solid Interactions and Laser Processing, S. D. Ferris et al., Eds., AIP Conference Proceedings, Vol. 50, American Institute of Physics, New York, p. 232.Google Scholar
  152. E. Stürmer and M. von Allmen (1978), J. Appl. Phys.49, 5648.Google Scholar
  153. L. L. Sveshnikova, V. I. Donin, and S. M. Repinskii (1977), Sov. Phys. Tech. Phys. Lett.3, 223.Google Scholar
  154. D. T. Swift-Hook and A. E. F. Gick (1973), Weld. J.52, 492S.Google Scholar
  155. K. Takagi and M. Ishii (1977), J. Cryst. Growth40, 1.Google Scholar
  156. K. Takei, S. Fujimoni, and K. Nagai (1980), J. Appl. Phys.51, 2903.Google Scholar
  157. M. Terao, K. Shigematsu, M. Ojima, Y. Taniguchi, S. Horigome, and S. Yonezawa (1979), J. Appl. Phys.50, 6881.Google Scholar
  158. S. A. Thompson (1970), Electron. Eng.29, 48.Google Scholar
  159. L. E. Topol and R. A. Happe (1974),J. Non-Cryst. Solids15, 116.Google Scholar
  160. L. C. Towle, J. A. McKay, and J. T. Schriempf (1979),J. Appl. Phys.50, 4391.Google Scholar
  161. B. A. Tozer (1976), Opt. Laser Technol., April, p. 57.Google Scholar
  162. W-T Tsang and S. Wang (1975), Appl. Phys. Lett.27, 79.Google Scholar
  163. A. A. Uglov and A. N. Kokora (1977), Sov. J. Quantum Electron.7, 671.Google Scholar
  164. A. A. Uglov, A. N. Kotova, and N. V. Berlin (1978), Sov. J. Quantum Electron.8, 884.Google Scholar
  165. M. von Allmen (1976), J. Appl. Phys.47, 5460.Google Scholar
  166. R. J. von Gutfeld, E. E. Tynan, R. L. Melcher, and S. E. Blum (1979), Appl. Phys. Lett.35, 651.Google Scholar
  167. C. von Osenbruggen and Th. P. J. Botden (1975), Proceedings of the 2nd International Symposium of the Japanese Welding Society, Adv. Weld. Technol., p. 597.Google Scholar
  168. R. E. Wagner (1974),J. Appl. Phys.45, 4631.Google Scholar
  169. J. M. Webster (1970), Met. Progr.98, 59.Google Scholar
  170. W. W. Weick (1972), IEEE J. Quantum Electron.QE-8, 126.Google Scholar
  171. L. S. Weinman and J. N. Devant (1979), in Laser Solid Interactions and Laser Processing, S. D. Ferris et al., Eds. AIP Conference Proceedings, Vol. 50, American Institute of Physics, New York.Google Scholar
  172. L. S. Weinman, C. Kim, T. R. Tucker, and E. A. Metzbower (1978), Appl. Opt.17, 906.Google Scholar
  173. D. M. Wick (1975), Paper MR-75–491, Soc. Man. Engineers.Google Scholar
  174. T. J. Wieting and J. L. de Rosa (1979), J. Appl. Phys.50, 1071.Google Scholar
  175. T. J. Wieting and J. T. Schriempf (1976), J. Appl. Phys.47, 4009.Google Scholar
  176. R. A. Willgoss, J. H. P. C. Megaw, and J. M. Clark (1979), Opt. Laser Technol., April, p. 73.Google Scholar
  177. J. R. Williamson (1976), in Industrial Applications of High Power Laser Technology, Vol. 86, J. F. Ready, Ed., Proceedings of the Society of Photo-Optical Instrument Engineers, Palo Verdes Estates, California.Google Scholar
  178. J. H. Wood (1977), Microelectron. Symp., p. 81.Google Scholar
  179. V. J. Zaleckas and J. C. Koo (1977), Appl. Phys. Lett.31, 615.Google Scholar
  180. D. M. Zehner, C. W. White, and G. W. Ownby (1980), Appl. Phys. Lett.36, 56.Google Scholar

Copyright information

© Plenum Press, New York 1983

Authors and Affiliations

  • W. W. Duley
    • 1
  1. 1.York UniversityTorontoCanada

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