Estructura Cristalina De Cobre 6o2821

Ciencia e Ingeniería Neogranadina ISSN: 0124-8170 [email protected] Universidad Militar Nueva Granada Colombia

Duque Jaramaillo, Jaime; Llano Sánchez, Luis Eduardo; Villazón Amaris, Hernando Estructura cristalina del cobre, propiedades microscópicas mecánicas y de procesamiento Ciencia e Ingeniería Neogranadina, vol. 16, núm. 2, agosto-diciembre, 2006, pp. 96-103 Universidad Militar Nueva Granada Bogotá, Colombia

Disponible en: http://www.redalyc.org/articulo.oa?id=91116210

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Sistema de Información Científica Red de Revistas Científicas de América Latina, el Caribe, España y Portugal Proyecto académico sin fines de lucro, desarrollado bajo la iniciativa de abierto

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WŽƌŵĞĚŝŽĚĞůĂŽďƐĞƌǀĂĐŝſŶŵĞƚĂůŽŐƌĄĮĐĂƐĞďƵƐĐĂ ůŵĂƚĞƌŝĂůĞƐƚƵĚŝĂĚŽĞƐůĄŵŝŶĂĚĞĐŽďƌĞĞůĞĐƚƌŽůşƟĐŽ ǀĞƌ ĨĂƐĞƐ ƉƌĞƐĞŶƚĞƐ͕ ĚŝƐƚƌŝďƵĐŝſŶ ĚĞ ĨĂƐĞƐ͕ ŐƌĂŶŽƐ͕ ĐŽŶƵŶĂƉƵƌĞnjĂĚĞσσ͕σй͘ ƚĂŵĂŹŽ ƉƌŽŵĞĚŝŽ ĚĞ ŐƌĂŶŽ͕ ĨŽƌŵĂ ĚĞ ŐƌĂŶŽ͘ ^ŝŶ ĞŵďĂƌŐŽ͕ĂůƚƌĂƚĂƌƐĞĚĞƵŶŵĂƚĞƌŝĂůσσ͕σйƉƵƌŽƐŽůĂͲ ͘DĠƚŽĚŽƐ ŵĞŶƚĞƐĞŽďƐĞƌǀĂůĂƉƌĞƐĞŶĐŝĂĚĞƵŶĂĨĂƐĞĐŽŶƟŶƵĂ ůĞƐƚƵĚŝŽĚĞůĂĞƐƚƌƵĐƚƵƌĂĐƌŝƐƚĂůŝŶĂƐĞŚĂĐĞƉŽƌŵĞͲ ĚĞ ĐŽďƌĞ͘ WŽƌ ĞƐƚŽ ŵŝƐŵŽ͕ ŶŽ ƐĞ ĞǀŝĚĞŶĐŝĂŶ ĨĄĐŝůͲ ĚŝŽ ĚĞ ƉƌƵĞďĂƐ ŵĞƚĂůŽŐƌĄĮĐĂƐ LJ ĚĞ ŵŝĐƌŽƐĐŽƉşĂ ĚĞ ŵĞŶƚĞ ŐƌĂŶŽƐ ŝŶĚŝǀŝĚƵĂůĞƐ ĚĞů ŵĂƚĞƌŝĂů Ăů ĂƵŵĞŶƚŽ ƚƌĂŶƐŵŝƐŝſŶĚĞĞůĞĐƚƌŽŶĞƐdD;dƌĂŶƐŵŝƐŝŽŶůĞĐƚƌŽŶ ƵƟůŝnjĂĚŽ;λκκyͿ;sĞƌ&ŝŐƵƌĂνͿ͘ DŝĐƌŽƐĐŽƉLJͿ͘ WŽƌŵĞĚŝŽĚĞůĂŵĞƚĂůŽŐƌĂİĂƐŽůĂŵĞŶƚĞƐĞŽďƐĞƌǀĂͲ λ͘DĞƚĂůŽŐƌĂİĂ ƌŽŶ ĞĨĞĐƚŽƐ ŵŝĐƌŽƐĐſƉŝĐŽƐ ĚĞ ŽƌŝĞŶƚĂĐŝſŶ͘ >Ă &ŝŐƵͲ >ĂŵƵĞƐƚƌĂƐĞƉƵůĞƉŽƌŵĞĚŝŽĚĞůŝũĂƐμκκ͕ξκκLJπκκ ƌĂξĨƵĞƚŽŵĂĚĂĚĞůĂŵƵĞƐƚƌĂĚĞĐŽďƌĞůŝũĂĚĂƉĞƌŽ LJĚĞƐƉƵĠƐĞŶƉĂŹŽƵƟůŝnjĂŶĚŽĂůƷŵŝŶĂĐŽŵŽŵĂƚĞƌŝĂů ƐŝŶ ĂƚĂƋƵĞ ƋƵşŵŝĐŽ͘ Ŷ ĞůůĂ ƐĞ ƉƵĞĚĞ ŽďƐĞƌǀĂƌ ƵŶĂ ĂďƌĂƐŝǀŽ͘WŽƐƚĞƌŝŽƌŵĞŶƚĞ͕ůĂŵƵĞƐƚƌĂƐĞĂƚĂĐĂƋƵşŵŝͲ ŽƌŝĞŶƚĂĐŝſŶ ƉƌĞĨĞƌĞŶĐŝĂů ĚĞů ŵĂƚĞƌŝĂů ĞŶ ĚŝƌĞĐĐŝſŶ ĐĂŵĞŶƚĞĐŽŶƵŶĂƐŽůƵĐŝſŶĚĞĐůŽƌƵƌŽĨĠƌƌŝĐŽĂůνйĞŶ ůŽŶŐŝƚƵĚŝŶĂůĚĞďŝĚĂĂůƉƌŽĐĞƐŽĚĞůĂŵŝŶĂĐŝſŶ͕ĞůĐƵĂů ǀŽůƵŵĞŶ͘ŶƐĂLJŽƌĞĂůŝnjĂĚŽĞŶůŽƐůĂďŽƌĂƚŽƌŝŽƐĚĞůĂ ŝŶĚƵĐĞƵŶĂůĂƌŐĂŵŝĞŶƚŽĚĞůŽƐŐƌĂŶŽƐLJŽƌŝĞŶƚĂĐŝſŶ hŶŝǀĞƌƐŝĚĂĚDŝůŝƚĂƌEƵĞǀĂ'ƌĂŶĂĚĂ͘ ĞŶůĂĚŝƌĞĐĐŝſŶĚĞůĂŵŝŶĂĐŝſŶ͘ŶůĂŝŵĂŐĞŶƚĂŵďŝĠŶ ƐĞŽďƐĞƌǀĂŶƵŶĂƐůşŶĞĂƐŽƐĐƵƌĂƐŵĂƌĐĂĚĂƐƚŽĚĂƐĐŽŶ μ͘DŝĐƌŽƐĐŽƉşĂĚĞdƌĂŶƐŵŝƐŝſŶĚĞůĞĐƚƌŽŶĞƐdD ƵŶĂŵŝƐŵĂŽƌŝĞŶƚĂĐŝſŶ͕ƌĞƐƵůƚĂĚŽĚĞůƉƌŽĐĞƐŽĚĞƉƵͲ >Ă ŵƵĞƐƚƌĂ ƉĂƌĂ ĂŶĄůŝƐŝƐ ƟĞŶĞ ƵŶ ĞƐƉĞƐŽƌ ŵĞŶŽƌ Ă ůŝĚŽĚĞůĂƐƵƉĞƌĮĐŝĞĚĞůĐŽďƌĞ;ŵĂƚĞƌŝĂůŵƵLJďůĂŶĚŽ͕ μκκʅŵĐŽŶĞůĐƵĂůƐĞĂůĐĂŶnjĂƵŶĂƌĞŐŝſŶ͞ĞůĞĐƚƌſͲ ĚƵƌĞnjĂ DŽŚƐ ĚĞ μ͕ς͘ οκ Ͳ ςκ ,EͿ͕ Ğů ĐƵĂů ĞƐ ŵƵLJ ŶŝĐĂŵĞŶƚĞƚƌĂŶƐƉĂƌĞŶƚĞ͟ƉĂƌĂůůĞǀĂƌĂĐĂďŽůĂŽďƐĞƌͲ ĂŐƌĞƐŝǀŽLJƋƵĞĚĂĐŽŶĞƐƚĂƐŝŵƉƌĞƐŝŽŶĞƐƐƵƉĞƌĮĐŝĂůĞƐ ǀĂĐŝſŶ͘ ŵƵLJĨĄĐŝůŵĞŶƚĞ΀ξ΁͘ ůĞƋƵŝƉŽƵƟůŝnjĂĚŽĞƐƵŶdE/'͘ĞŶůŽƐ>ĂďŽƌĂƚŽͲ ƌŝŽƐ ĚĞ ůĂ hŶŝǀĞƌƐŝĚĂĚ EĂĐŝŽŶĂů ĚĞ ŽůŽŵďŝĂ͕ ĞŶ ůĂ ƐĞĚĞŽŐŽƚĂ͘^ĞŚĂĐĞůĂůĞĐƚƵƌĂĚĞůĂŵƵĞƐƚƌĂƚĞŶŝĞŶͲ ĚŽƵŶĂŝŶĐůŝŶĂĐŝſŶĚĞцλκΣĐŽŶƌĞƐƉĞĐƚŽĂůĂŚŽƌŝnjŽŶͲ ƚĂů͕ƚĞŵƉĞƌĂƚƵƌĂĚĞλςΣLJƵŶĂŵďŝĞŶƚĞĚĞǀĂĐşŽĚĞ λκͲξdŽƌ͘ ν͘WƌƵĞďĂƐDĞĐĄŶŝĐĂƐĚĞZĞƐŝƐƚĞŶĐŝĂĂůĂdƌĂĐĐŝſŶ >Ă ĞǀĂůƵĂĐŝſŶ ĚĞ ƉƌŽƉŝĞĚĂĚĞƐ ŵĞĐĄŶŝĐĂƐ Ă ƚĞŶƐŝſŶ ĚĞůĂůĄŵŝŶĂƐĞŚŝnjŽĞŶƵŶĂŵĄƋƵŝŶĂ/E^dZKEĂƵŶĂ ǀĞůŽĐŝĚĂĚĚĞλμ͕οŵŵͬŵŝŶ͘ŶůŽƐ>ĂďŽƌĂƚŽƌŝŽƐĚĞůĂ hŶŝǀĞƌƐŝĚĂĚĚĞůŽƐŶĚĞƐ͘

///͘Z^h>dK^ ů ĞƐƚƵĚŝŽ ĚĞ ůĂ ŵŝĐƌŽĞƐƚƌƵĐƚƵƌĂ ĚĞů ĐŽďƌĞ ƐĞ ůůĞǀſ &ŝŐƵƌĂν͘^ƵƉĞƌĮĐŝĞĚĞĐŽďƌĞ͘ŶĞůĐşƌĐƵůŽƐĞŽďƐĞƌǀĂŶŐƌĂŶŽƐĚĞ ĂĐĂďŽĐŽŶůĂĂLJƵĚĂĚĞĚŽƐƚĠĐŶŝĐĂƐĚŝƐƟŶƚĂƐ͕ůĂŵŝͲ ŵĂƚĞƌŝĂůĐŽŶĂůŐƷŶŐƌĂĚŽĚĞĂůĂƌŐĂŵŝĞŶƚŽLJĐŝĞƌƚĂŽƌŝĞŶƚĂĐŝſŶ ĐƌŽƐĐŽƉşĂĚĞƚƌĂŶƐŵŝƐŝſŶĞůĞĐƚƌſŶŝĐĂLJƉŽƌŵĞĚŝŽĚĞ



9RO1R‡'LFLHPEUH

81,9(56,'$'0,/,7$518(9$*5$1$'$

ůĂŵŝŶĂĐŝſŶ͕ ƐŝŶ ĞŵďĂƌŐŽ ŶŽ ƐĞ ƉƵĞĚĞ ĂĮƌŵĂƌ ĞƐƚŽ ƚĞŶŝĞŶĚŽĞŶĐƵĞŶƚĂƐŽůĂŵĞŶƚĞůĂƉƌƵĞďĂĚĞdD͘ >Ă ĮŐƵƌĂ πď ŵƵĞƐƚƌĂ ǀĂƌŝŽƐ ŐƌĂŶŽƐ ĐŽŶ ĚŝĨĞƌĞŶƚĞƐ ŽƌŝĞŶƚĂĐŝŽŶĞƐ͕ƋƵĞƐĞĞǀŝĚĞŶĐŝĂŶƉŽƌĐĂŵďŝŽƐĚĞĐŽͲ ůŽƌ͘ >ĂĮŐƵƌĂπĐŵƵĞƐƚƌĂƵŶŐƌƵƉŽĚĞŝŵƉĞƌĨĞĐĐŝŽŶĞƐĚĞ ůşŶĞĂ ƵďŝĐĂĚĂƐ ĞŶ Ğů ĐŽŶƚŽƌŶŽ ĚĞ ůĂ ŵƵĞƐƚƌĂ͘ ƐƚŽƐ ĚĞĨĞĐƚŽƐƐĞĂƐŽĐŝĂŶĂĚŝƐůŽĐĂĐŝŽŶĞƐĚĞďŽƌĚĞ;ĐŽŶƐĞƌͲ ǀĂƟǀĂƐͿĚĞďŝĚĂƐĂůĂŝŶƐĞƌĐŝſŶĚĞůşŶĞĂƐĚĞĄƚŽŵŽƐĞŶ ůĂĞƐƚƌƵĐƚƵƌĂĚĞůĐƌŝƐƚĂů͘ &ŝŐƵƌĂξ͘KƌŝĞŶƚĂĐŝſŶĚĞŐƌĂŶŽƐĞŶůĄŵŝŶĂĚĞĐŽďƌĞĞůĞĐƚƌŽůşƟĐŽ͘ /ŵĂŐĞŶĂλκκy

ŶůĂ&ŝŐƵƌĂοƐĞƉƵĞĚĞĂƉƌĞĐŝĂƌůĂŽƌŝĞŶƚĂĐŝſŶƉƌĞͲ ƐĞŶƚĞĞŶůŽƐƐĞŶƟĚŽƐůŽŶŐŝƚƵĚŝŶĂůLJƚƌĂŶƐǀĞƌƐĂů

ŶůĂĮŐƵƌĂπĚƐĞŽďƐĞƌǀĂŶĞŶĞůĨŽŶĚŽĚĞĐŽůŽƌǀĞƌĚĞ ŽƐĐƵƌŽůĂƐůşŶĞĂƐĚĞďŽƌĚĞĚĞŐƌĂŶŽ͘>ĂƐůşŶĞĂƐŽƐĐƵͲ ƌĂƐ ƐŽŶ ĚŝƐůŽĐĂĐŝŽŶĞƐ ĨŽƌŵĂŶĚŽ ƵŶ ƉŽƐŝďůĞ ďŽƐƋƵĞ ĚĞĚŝƐůŽĐĂĐŝŽŶĞƐ͘

&ŝŐƵƌĂο͘KƌŝĞŶƚĂĐŝſŶƉƌĞĨĞƌĞŶĐŝĂůĚĞůŽƐŐƌĂŶŽƐĚĞĂĐƵĞƌĚŽĐŽŶ ůĂĚŝƌĞĐĐŝſŶĚĞůĂŵŝŶĂĚŽ

&ŝŐƵƌĂπ/ŵĄŐĞŶĞƐŽďƚĞŶŝĚĂƐĐŽŶĞůdDĂλρκκκyƉĂƌĂĂLJďLJ οοκκκyƉĂƌĂĐLJĚ͘ĂͿ'ƌĂŶŽƐĂůĂƌŐĂĚŽƐĚĞĐŽďƌĞĐŽŶĂůŐƷŶŐƌĂͲ ĚŽĚĞŽƌŝĞŶƚĂĐŝſŶ͘ďͿKƌŝĞŶƚĂĐŝſŶĚĞŐƌĂŶŽƐĚĞĐŽďƌĞ͘ĐͿĞĨĞĐƚŽƐ ĚĞůşŶĞĂ;νͿ͘ĚͿŽƌĚŝůůĞƌĂĚĞĚĞĨĞĐƚŽƐ͘;>Ăď͘hEƐĞĚĞďŽŐŽƚĂͿ

͘dD

>Ă &ŝŐƵƌĂ ρ ŝůƵƐƚƌĂ ĚŝĨĞƌĞŶƚĞƐ ƟƉŽƐ ĚĞ ĚŝƐůŽĐĂĐŝŽŶĞƐ WŽƌŵĞĚŝŽĚĞĞƐƚĂƚĠĐŶŝĐĂƐĞĞƐƚĄŶĞǀŝĚĞŶĐŝĂŶĚŽůĂƐ ĞŶĐŽŶƚƌĂĚĂƐĞŶůĂŵƵĞƐƚƌĂ͘>ĂĮŐƵƌĂρĂŵƵĞƐƚƌĂƵŶĂ ŝŵƉĞƌĨĞĐĐŝŽŶĞƐƉƌĞƐĞŶƚĞƐĞŶĞůŵĂƚĞƌŝĂů͘ŶůĂƐŝŵĄͲ ŵĂŐŶŝĮĐĂĐŝſŶĚĞƉŽƐŝďůĞƐďŽƐƋƵĞƐĚĞĚŝƐůŽĐĂĐŝŽŶĞƐ͕ ŐĞŶĞƐƐĞŽďƐĞƌǀĂŶĚŝƐůŽĐĂĐŝŽŶĞƐĚĞůşŶĞĂ͘ ƋƵĞƐĞŽďƐĞƌǀĂŶĐŽŵŽĐŽƌĚŝůůĞƌĂƐĞŶƵŶĞŶƚŽƌŶŽĐŽŶͲ ƟŶĞŶƚĂů͘^ĞĞŶĐƵĞŶƚƌĂŶƚĂŵďŝĠŶĂůŐƵŶĂƐĚŝƐůŽĐĂĐŝŽͲ λρκκκyƐĞŝĚĞŶƟĮĐĂƌŽŶĞŶůĂĮŐƵƌĂπĂĚŽƐŐƌĂŶŽƐ ŶĞƐ ĚĞ ůşŶĞĂ ƚƌĞŶnjĂĚĂƐ ;ρďͿ͕ ďŽƐƋƵĞƐ ĚĞ ĚŝƐůŽĐĂĐŝŽͲ ĚĞĐŽďƌĞĂůĂƌŐĂĚŽƐ͕ĐŽŶĐŝĞƌƚĂŽƌŝĞŶƚĂĐŝſŶ͘>ŽƐĚĞĨĞĐͲ ŶĞƐ LJ ƵŶĂƐ ĚŝƐůŽĐĂĐŝŽŶĞƐ ơƉŝĐĂƐ ĚĞů ĐŽďƌĞ ƌĞĐŽĐŝĚŽ ƚŽƐ ƉŽĚƌşĂŶ ŚĂďĞƌ ƐŝĚŽ ĐĂƵƐĂĚŽƐ ƉŽƌ Ğů ƉƌŽĐĞƐŽ ĚĞ ůĂƐĐƵĂůĞƐƟĞŶĞŶĨŽƌŵĂĚĞƚƌŝĚĞŶƚĞ͘ 9RO1R‡'LFLHPEUH

&,(1&,$(,1*(1,(5Ë$1(2*5$1$',1$

>ŽƐĚĂƚŽƐŽďƚĞŶŝĚŽƐƉĂƌĂůĂƐƉƌŽďĞƚĂƐůŽŶŐŝƚƵĚŝŶĂůĞƐ ƐĞƉƌĞƐĞŶƚĂŶĞŶůĂdĂďůĂλ͕ŵŝĞŶƚƌĂƐƋƵĞůŽƐĐŽƌƌĞƐͲ ƉŽŶĚŝĞŶƚĞƐĂƉƌŽďĞƚĂƐƚƌĂŶƐǀĞƌƐĂůĞƐ͕ƐĞŵƵĞƐƚƌĂŶĞŶ ůĂdĂďůĂμ͘ >ŽƐǀĂůŽƌĞƐĚĞĐĂƌŐĂLJĞůŽŶŐĂĐŝſŶŵĄdžŝŵĂLJŵſĚƵůŽ ĚĞĞůĂƐƟĐŝĚĂĚ͕ĞƐƚĄŶŝŶĐůƵŝĚŽƐĞŶůĂƐƚĂďůĂƐ͘ dĂďůĂλ͘ĂƚŽƐĚĞƚƌĂĐĐŝſŶƉĂƌĂůĂƐƉƌŽďĞƚĂƐĞŶĚŝƌĞĐĐŝſŶůŽŶŐŝƚƵĚŝŶĂů

&ŝŐƵƌĂρ͘ĞĨĞĐƚŽƐĞŶĞůĐŽďƌĞĂοοκκκyƉĂƌĂĂ͕ďLJĐLJĂμοοκκy ƉĂƌĂĚ͘ĂͿDĂŐŶŝĮĐĂĐŝſŶĚĞůĂĐŽƌĚŝůůĞƌĂĚĞĚŝƐůŽĐĂĐŝŽŶĞƐ͘ďͿŵͲ ƉůŝĂĐŝſŶĚĞĚŝƐůŽĐĂĐŝŽŶĞƐĚĞůşŶĞĂƚƌĞŶnjĂĚĂƐ͘ĐͿĞĨĞĐƚŽơƉŝĐŽĚĞ ĐŽďƌĞƌĞĐŽĐŝĚŽ;ƚƌŝĚĞŶƚĞͿ͘ĚͿŽƐƋƵĞĚĞĚŝƐůŽĐĂĐŝŽŶĞƐ͘ŽƌĚĞƐĚĞ ŐƌĂŶŽ͘&ƌĂŶũĂƐĚĞĐƵƌǀĂƚƵƌĂ͘;>Ăď͘hEƐĞĚĞŽŐŽƚĄͿ

>ĂĮŐƵƌĂρĐƐĞŽďƐĞƌǀĂƵŶƚƌŝĚĞŶƚĞĐŽŶĨŽƌŵĂĚŽƉŽƌ dĂďůĂμ͘ĂƚŽƐĚĞƚƌĂĐĐŝſŶƉĂƌĂůĂƐƉƌŽďĞƚĂƐĞŶĚŝƌĞĐĐŝſŶƚƌĂŶƐǀĞƌƐĂů ĚŽƐĚŝƐůŽĐĂĐŝŽŶĞƐĚĞďŽƌĚĞĐŽŶĞĐƚĂĚĂƐƉŽƌƵŶĂĚŝƐůŽͲ ĐĂĐŝſŶĚĞďŽƌĚĞŝŶŝĐŝĂů͘ƐƚĞƟƉŽĚĞĚĞĨĞĐƚŽĞƐơƉŝĐŽ ĚĞů Ƶ ƌĞĐŽĐŝĚŽ LJ ƉƌŽďĂďůĞŵĞŶƚĞ ƚĂŵďŝĠŶ ƐĞ ĚĞďĞ ƉƌĞƐĞŶƚĂƌ ĞŶ ŵĂƚĞƌŝĂůĞƐ ĐŽŶ ĞƐƚƌƵĐƚƵƌĂ ĐƌŝƐƚĂůŝŶĂ &͘ >Ă &ŝŐƵƌĂ ρĚ ĞƐ ŵƵLJ ŝŶƚĞƌĞƐĂŶƚĞ ĚĂĚŽ ƋƵĞ ĞŶ ĞƐƚĂ ŝŵĂŐĞŶ ƐĞ ƉƵĞĚĞŶ ŽďƐĞƌǀĂƌ ƐŝŵƵůƚĄŶĞĂŵĞŶƚĞ ƵŶ ŐƌĂŶ ďŽƐƋƵĞ ĚĞ ĚŝƐůŽĐĂĐŝŽŶĞƐ ũƵŶƚŽ ĐŽŶ ďŽƌĚĞƐ ĚĞ ŐƌĂŶŽLJ͞ĞƐƚƌşĂƐ͘͟>ĂƐĞƐƚƌşĂƐƐŽŶĨƌĂŶũĂƐĚĞĐŽŶƚŽƌŶŽ ĞŶĨŽƌŵĂĚĞƉĂůŽŵĂƐƋƵĞƐĞƉƌŽĚƵĐĞŶƉŽƌĂĐƵŵƵůĂͲ ĐŝŽŶĞƐĚĞĄƚŽŵŽƐƋƵĞŶŽŚĂŶƚĞŶŝĚŽĞůƟĞŵƉŽƐƵĮͲ ĐŝĞŶƚĞĚĞĚŝĨƵŶĚŝƌƐĞLJƌĞŽƌŐĂŶŝnjĂƌƐĞƉĂƌĂƌĞĐƵƉĞƌĂƌůĂ ĞƐƚƌƵĐƚƵƌĂĐƌŝƐƚĂůŝŶĂ͘ƐƚĂƐƉƌŽďĂďůĞŵĞŶƚĞƐĞƉƌŽĚƵͲ ũĞƌŽŶƉŽƌůĂĚŝĨĞƌĞŶĐŝĂĚĞĞƐƉĞƐŽƌĞƐĞŶůĂŵƵĞƐƚƌĂLJ ĞůƚƌĂƚĂŵŝĞŶƚŽƚĠƌŵŝĐŽ͘

͘WƌƵĞďĂƐĚĞdĞŶƐŝſŶ ƐƚŽƐĞŶƐĂLJŽƐĨƵĞƌŽŶƌĞĂůŝnjĂĚŽƐĞŶůŽƐ>ĂďŽƌĂƚŽƌŝŽƐ ĚĞůĂhŶŝǀĞƌƐŝĚĂĚĚĞůŽƐŶĚĞƐ͘

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>ĂdĂďůĂνŵƵĞƐƚƌĂůŽƐǀĂůŽƌĞƐĚĞƌĞƐŝůŝĞŶĐŝĂ͕ƚĞŶĂĐŝͲ ĚĂĚ LJ ƉŽƌĐĞŶƚĂũĞƐ ĚĞ ĞůŽŶŐĂĐŝſŶ LJ ĚĞ ƌĞĚƵĐĐŝſŶ ĚĞ ĄƌĞĂŽďƚĞŶŝĚŽƐ dĂďůĂν͘sĂůŽƌĞƐĚĞƌĞƐŝůŝĞŶĐŝĂLJƚĞŶĂĐŝĚĂĚ

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ŶůĂ&ŝŐƵƌĂλκƐĞĞǀŝĚĞŶĐŝĂůĂĞůĞǀĂĚĂĐĂƉĂĐŝĚĂĚĚĞ ĂůŵĂĐĞŶĂŵŝĞŶƚŽ ĚĞ ĞŶĞƌպà ĚĞů ŵĂƚĞƌŝĂů͕ ƉƌĞƐĞŶͲ ƚĄŶĚŽƐĞ ĞŶ ůĂ ŵĂĐƌŽĞƐƚƌƵĐƚƵƌĂ ĂůƚĂƐ ĚĞĨŽƌŵĂĐŝŽŶĞƐ ƉůĄƐƟĐĂƐ͕ĂƵŶƋƵĞĞůŵĂƚĞƌŝĂůŶŽƉƌĞƐĞŶƚĞƵŶĂĂůƚĂƌĞͲ ƐŝůŝĞŶĐŝĂ͘ƐƚĞŵĂĐƌŽĞĨĞĐƚŽƐƵƌŐĞĐŽŵŽĐŽŶƐĞĐƵĞŶĐŝĂ ĚĞůĂĞƐƚƌƵĐƚƵƌĂŝŶƚĞƌŶĂĚĞůŵĂƚĞƌŝĂůLJĚĞůĂĂĐƟǀĂĐŝſŶ ĚĞƐŝƐƚĞŵĂƐĚĞĚĞƐůŝnjĂŵŝĞŶƚŽ͘

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͘ƐƚƌƵĐƚƵƌĂǀƐ͘WƌŽƉŝĞĚĂĚĞƐ ŽŶďĂƐĞĞŶĞůĐŽŵƉŽƌƚĂŵŝĞŶƚŽĞdžŚŝďŝĚŽƉŽƌĞůŵĂͲ >ĂnjŽŶĂĚĞĚĞĨŽƌŵĂĐŝſŶĞůĄƐƟĐĂĞƐĞƐƚƌĞĐŚĂLJĂƋƵĞ ƚĞƌŝĂůĂůƐĞƌƐŽŵĞƟĚŽĂƚƌĂĐĐŝſŶ͕ƐĞŚĂĐĞŶĞǀŝĚĞŶƚĞƐ ĂůƐĞƌƵŶŵĂƚĞƌŝĂůσσ͕σйƉƵƌŽŶŽƟĞŶĞƵŶĂĐĂŶƟĚĂĚ ŝŵƉŽƌƚĂŶƚĞĚĞŝŵƉĞƌĨĞĐĐŝŽŶĞƐƋƵĞĂƵŵĞŶƚĞůĂĐĂŶͲ ůĂƐĚŝĨĞƌĞŶƚĞƐũĞƌĂƌƋƵşĂƐĞƐƚƌƵĐƚƵƌĂůĞƐĚĞůŵĂƚĞƌŝĂů͘ 9RO1R‡'LFLHPEUH

&,(1&,$(,1*(1,(5Ë$1(2*5$1$',1$

ƟĚĂĚ ĚĞ ĞŶĞƌպà ƌĞƋƵĞƌŝĚĂ ƉĂƌĂ ĞŵƉĞnjĂƌ Ă ĐĂƵƐĂƌ ͘WƌŽƉŝĞĚĂĚĞƐǀƐ͘WƌŽĐĞƐĂŵŝĞŶƚŽ ŵŽǀŝŵŝĞŶƚŽƐĂƚſŵŝĐŽƐ͘ŶĞƐƚĂƐĚŽƐƉƌŝŵĞƌĂƐƉƌĞǀĂͲ ůĐŽďƌĞĚĞďŝĚŽĂƐƵĞƐƚƌƵĐƚƵƌĂĂƚſŵŝĐĂLJŽƌŐĂŶŝnjĂͲ ůĞĐĞůĂũĞƌĂƌƋƵşĂŶĂŶŽĐƌŽƐĐſƉŝĐĂĚĞůŵĂƚĞƌŝĂů͘ ĐŝſŶĞƐƉĂĐŝĂůƉŽƐĞĞƵŶĂĂůƚĂĐĂƉĂĐŝĚĂĚĚĞĚĞĨŽƌŵĂͲ ĐŝſŶ ƉůĄƐƟĐĂ͕ ƉŽƌ ůŽ ĐƵĂů ƉĂƌĂ ƐƵ ƉƌŽĐĞƐĂŵŝĞŶƚŽ ƐĞ >ĂŵŽǀŝůŝnjĂĐŝſŶĚĞĚŝƐůŽĐĂĐŝŽŶĞƐĞŶůĂĞƐƚƌƵĐƚƵƌĂĞƐƚĄ ƵƟůŝnjĂŶ ƉƌĞĨĞƌŝďůĞŵĞŶƚĞ ŵĠƚŽĚŽƐ ĚĞ ĚĞĨŽƌŵĂĐŝſŶ ƌĞůĂĐŝŽŶĂĚĂĐŽŶůĂĂĐƟǀĂĐŝſŶĚĞƐŝƐƚĞŵĂƐĚĞĚĞƐůŝnjĂͲ ƉůĄƐƟĐĂ ĐŽŵŽ Ğů ƚƌĞĮůĂĚŽ LJ Ğů ůĂŵŝŶĂĚŽ͘ ƐƚĂƐ ƉƌŽͲ ŵŝĞŶƚŽ͕ĚĞůĂĨĂŵŝůŝĂ;λλλͿĐĂƌĂĐƚĞƌşƐƟĐĂĚĞůĂĞƐƚƌƵĐƚƵͲ ƉŝĞĚĂĚĞƐ͕ĂĚĞŵĄƐĚĞƐƵĐŽŶĚƵĐƟǀŝĚĂĚLJĂďƵŶĚĂŶĐŝĂ ƌĂ&ĚĞůĐŽďƌĞ͕ůĂĐƵĂůƐĞŚĂĐĞƉƌĞƐĞŶƚĞĞŶůĂĞƚĂƉĂ ĞŶůĂŶĂƚƵƌĂůĞnjĂ͕ƉĞƌŵŝƚĞŶƋƵĞƐĞĂŵƵLJƵƟůŝnjĂĚŽĞŶ ĚĞĚĞĨŽƌŵĂĐŝſŶƉůĄƐƟĐĂ͘ůůşƐĞŝŶŝĐŝĂĞůŵŽǀŝŵŝĞŶƚŽ ĐĂďůĞƐĚĞĐŽŶĚƵĐĐŝſŶĞůĠĐƚƌŝĐĂ͘ ĚĞůĂƐĚŝƐůŽĐĂĐŝŽŶĞƐĚĞůşŶĞĂLJĚĞƚŽƌŶŝůůŽ͕ĐĂƵƐĂŶĚŽ ƵŶĞĨĞĐƚŽŵĂĐƌŽƐĐſƉŝĐŽĚĞĚĞĨŽƌŵĂĐŝſŶ͘>ĂnjŽŶĂĚĞ ͘ƐƚƌƵĐƚƵƌĂʹWƌŽƉŝĞĚĂĚĞƐͲWƌŽĐĞƐĂŵŝĞŶƚŽ ĚĞĨŽƌŵĂĐŝſŶƉůĄƐƟĐĂĞƐĂŵƉůŝĂĚĞďŝĚŽĂƋƵĞůĂŵŽͲ λ͘ƉůŝĐĂĐŝŽŶĞƐ ǀŝůŝnjĂĐŝſŶĚĞĚŝƐůŽĐĂĐŝŽŶĞƐƐĞĨĂĐŝůŝƚĂƉŽƌĐĂƵƐĂĚĞůĂ ŶůĂƐŶƵĞǀĂƐƚĞŶĚĞŶĐŝĂƐĚĞŵŝŶŝĂƚƵƌŝnjĂĐŝſŶĚĞĐŽŵͲ ƉƵƌĞnjĂĚĞůŵĂƚĞƌŝĂů͕ůĂĐƵĂůĞǀŝƚĂůĂƉƌĞƐĞŶĐŝĂĚĞĨĞͲ ƉŽŶĞŶƚĞƐ ĞůĞĐƚƌſŶŝĐŽƐ LJ ƐĞŶƐſƌŝĐĂ Ğů ĐŽďƌĞ ĞƐ ƵƟůŝͲ ŶſŵĞŶŽƐĚĞĞŶĚƵƌĞĐŝŵŝĞŶƚŽƉŽƌƐŽůƵĐŝſŶLJƉŽƌƉƌĞͲ njĂĚŽ ŶŽƌŵĂůŵĞŶƚĞ ĐŽŵŽ ĞůĞĐƚƌŽĚŽ ĞŶ ƉƌŽĐĞƐŽƐ ĚĞ ĞůĞĐƚƌŽĞƌŽƐŝſŶLJĞůĞĐƚƌŽͲĚĞƉŽƐŝĐŝſŶ΀π΁͕ƐŝŶĞŵďĂƌŐŽ ĐŝƉŝƚĂĐŝſŶ͘ ŶŽĞƐƵƟůŝnjĂĚŽĐŽŵŽĐŽŵƉŽŶĞŶƚĞ͘ >ĂĨƌĂĐƚƵƌĂĞƐƵŶĞĨĞĐƚŽŵĂĐƌŽƐĐſƉŝĐŽƋƵĞĞƐĞůƌĞͲ Ŷ ƚĞĐŶŽůŽŐşĂƐ ĚĞ ŵŝĐƌŽ LJ ŶĂŶŽ ƐŝƐƚĞŵĂƐ DD^ LJ ƐƵůƚĂĚŽĚĞůĂĮŶĂůŝnjĂĐŝſŶĚĞůŽƐƉƌŽĐĞƐŽƐĚĞĚĞĨŽƌŵĂͲ ED^ƌĞƐƉĞĐƟǀĂŵĞŶƚĞ͕ĞůĐŽďƌĞƉŽĚƌşĂƐĞƌĞƐƚƵĚŝĂͲ ĐŝſŶƉůĄƐƟĐĂĚĞďŝĚŽĂƋƵĞůĂƐĚŝƐůŽĐĂĐŝŽŶĞƐLJĂŶŽƐĞ ĚŽ ƉĂƌĂ ƐĞƌ ƵƟůŝnjĂĚŽ ĐŽŵŽ ƐŽƉŽƌƚĞ͕ ĞƐƉĞĐŝĂůŵĞŶƚĞ ƉƵĞĚĞŶŵŽǀĞƌŵĄƐ͘ ĞŶED^ĚŽŶĚĞƐĞƌĞƋƵŝĞƌĞƵŶĂŵĂLJŽƌǀĞƌƐĂƟůŝĚĂĚ ŶůĂ&ŝŐƵƌĂλλƐĞƉƵĞĚĞŶŽďƐĞƌǀĂƌůĂƐnjŽŶĂƐŵĞŶĐŝŽͲ ŶĂĚĂƐ͘

&ŝŐƵƌĂλλ͘'ƌĄĮĐŽĐŽŵƉĂƌĂƟǀŽĚĞĚĞĨŽƌŵĂĐŝſŶǀƐ͘ĂǀĂŶĐĞĚĞůĞŶͲ ƐĂLJŽƉĂƌĂůĂƉƌŽďĞƚĂλĞŶĚŝƌĞĐĐŝſŶůŽŶŐŝƚƵĚŝŶĂů͘

9RO1R‡'LFLHPEUH

ĚĞůŽƐŵĂƚĞƌŝĂůĞƐĚĞďŝĚŽĂůĂĂůƚĂĞƐƉĞĐŝĮĐŝĚĂĚĚĞůĂ ĂƉůŝĐĂĐŝſŶ͘ >ĂƐ ĐĂƌĂĐƚĞƌşƐƟĐĂƐ ĚĞů ĐŽďƌĞ ĞůĞĐƚƌŽůşƟͲ ĐŽĐŽŵŽůĂĐĂƐŝŝĚĞĂůŝĚĂĚĚĞĞƐƚƌƵĐƚƵƌĂĐƌŝƐƚĂůŝŶĂ͕ůĂ ĐŽŶĚƵĐƟǀŝĚĂĚĞůĠĐƚƌŝĐĂƋƵĞƉŽƐĞĞLJůĂĨĂĐŝůŝĚĂĚĚĞƐƵ ŵĂŶƵĨĂĐƚƵƌĂ͕ ƐŽŶ ŵƵLJ ĚĞƐĞĂďůĞƐ ƉĂƌĂ ůŽƐ ƐŽƉŽƌƚĞƐ ΀ν΁͖ƐŝŶĞŵďĂƌŐŽ͕ƉƌĞƐĞŶƚĂƉƌŽďůĞŵĂƐĐŽŶƌĞƐƉĞĐƚŽĂ ůĂĞƐƚĂďŝůŝĚĂĚŵĞĐĄŶŝĐĂ͕ƉŽƌƐƵĂůƚĂĚƵĐƟůŝĚĂĚ͕ĐŽŶĞů ĐŽĞĮĐŝĞŶƚĞĚĞĞdžƉĂŶƐŝſŶƚĠƌŵŝĐĂ͕LJůĂŚŝƐƚĠƌĞƐŝƐŵĞͲ ĐĄŶŝĐĂ͘ ^ŝ ƐĞ ĚŽƉĂƌĂ Ğů ŵĂƚĞƌŝĂů ĐŽŶ ĞůĞŵĞŶƚŽƐ ƋƵĞ ĐŽŶƚƌŝďƵLJĂŶĂŵĞũŽƌĂƌĞƐƚĂƐĨĂůĞŶĐŝĂƐ͕ĞůĐŽďƌĞƉŽͲ ĚƌşĂĞŵƉůĞĂƌƐĞĐŽŵŽƐƵƐƚƌĂƚŽĞŶED^͘>ĂĞƐƚƌƵĐƚƵͲ ƌĂĐƌŝƐƚĂůŝŶĂĚĞůĐŽďƌĞĞƐďĂƐƚĂŶƚĞĂƉƚĂƉĂƌĂĞůĚŽƉĂͲ ũĞ͕LJĂƋƵĞƟĞŶĞƐŝƟŽƐƚĞƚƌĂĠĚƌŝĐŽƐĚŽŶĚĞƐĞƉƵĞĚĞŶ ĂůŽũĂƌĚŝǀĞƌƐŽƐƟƉŽƐĚĞĄƚŽŵŽƐ͘ ŶůĂ&ŝŐƵƌĂλμƐĞƉƌĞƐĞŶƚĂƵŶĞƐƉĞĐƚƌŽŐƌĂŵĂĐƵĂůŝƚĂͲ ƟǀŽĚĞůĐŽďƌĞĞůĞĐƚƌŽůşƟĐŽσσ͕σйƉƵƌŽ͕ĂůůşƐĞǀĞƋƵĞ ĂƵŶƋƵĞƟĞŶĞƵŶĂůƚŽŐƌĂĚŽĚĞƉƵƌĞnjĂƉƵĞĚĞĐŽŶƚĞͲ ŶĞƌ ĚŝǀĞƌƐĂƐ ŝŵƉƵƌĞnjĂƐ ĞŶ ƐƵ ĞƐƚƌƵĐƚƵƌĂ͕ ůĂƐ ĐƵĂůĞƐ ƉƵĞĚĞŶ ƐĞƌ ƐĞůĞĐĐŝŽŶĂĚĂƐ Ă ƉƌŽƉſƐŝƚŽ ĚĞ ĂĐƵĞƌĚŽ ĐŽŶůĂŶĞĐĞƐŝĚĂĚ͘

81,9(56,'$'0,/,7$518(9$*5$1$'$

KƚƌĂ ĂůƚĞƌŶĂƟǀĂ ƉĂƌĂ ŵĞũŽƌĂƌ ůĂƐ ƉƌŽƉŝĞĚĂĚĞƐ ĚĞů ĐŽďƌĞĐŽŵŽ ƐƵƐƚƌĂƚŽƉŽĚƌşĂ ƐĞƌƉŽƌ ŵĞĚŝŽ ĚĞĂůĞĂͲ ĐŝŽŶĞƐ ĐŽŶ njŝŶĐ ƉƌŽĚƵĐŝĞŶĚŽ ůĂƚŽŶĞƐ͕ LJ ĐŽŶ ĞƐƚĂŹŽ ƉĂƌĂŽďƚĞŶĞƌďƌŽŶĐĞƐ͕ĚĞĞƐƚĂŵĂŶĞƌĂƐĞŽďƟĞŶĞƵŶ ŵĂƚĞƌŝĂůŵĞĐĄŶŝĐĂŵĞŶƚĞŵĄƐĞƐƚĂďůĞĂůĂƵŵĞŶƚĂƌƐƵ ĚƵƌĞnjĂ΀ξ΁͘ůŽƌŽĞƐŵƵLJƵƟůŝnjĂĚŽĐŽŵŽŵĂƚĞƌŝĂůĞŶ ED^͕ĞƐƚĞƟĞŶĞƉƌŽƉŝĞĚĂĚĞƐƚĠƌŵŝĐĂƐ͕ĞůĠĐƚƌŝĐĂƐLJ ĚĞĚƵƌĞnjĂŵƵLJƐŝŵŝůĂƌĞƐĂůĂƐĚĞůĐŽďƌĞ͕ƐŝŶĞŵďĂƌŐŽ ůĂ ƉƌŝŶĐŝƉĂů ĚŝĨĞƌĞŶĐŝĂ ƌĂĚŝĐĂ ĞŶ ůŽƐ ŵĞĐĂŶŝƐŵŽƐ ĚĞ ŽdžŝĚĂĐŝſŶĚĞůŽƐŵĂƚĞƌŝĂůĞƐ͘DĞũŽƌĂŶĚŽĞƐƚĂĐĂƌĂĐƚĞͲ ƌşƐƟĐĂ͕ĞůĐŽďƌĞƉƵĞĚĞůůĞŐĂƌĂƐĞƌƵŶĂďƵĞŶĂĂůƚĞƌŶĂͲ ƟǀĂĞŶĞƐƚĞƟƉŽĚĞĂƉůŝĐĂĐŝſŶ͘

ŽƚƌŽƐŵĂƚĞƌŝĂůĞƐ͘ ĞďŝĚŽĂůĂĂŶŝƐŽƚƌŽƉşĂLJĂůĂƐƉƌŽƉŝĞĚĂĚĞƐƚĠƌŵŝĐĂƐ LJĞůĠĐƚƌŝĐĂƐƋƵĞƉƌĞƐĞŶƚĂĞůĐŽďƌĞƉƵĞĚĞƐĞƌƵƟůŝnjĂͲ ĚŽĞŶED^ƉĂƌĂƐĞŶƐĂƌƉƌŽƉŝĞĚĂĚĞƐĞŶĚŝĨĞƌĞŶƚĞƐ ĚŝƌĞĐĐŝŽŶĞƐ͘ Z&ZE/^ ΀λ΁>>E^͕d,KD^͘͞dŚĞ^ƚƌƵĐƚƵƌĞŽĨŵĂƚĞƌŝĂůƐ͘͟ D/d ƐĞƌŝĞƐ ŝŶ ŵĂƚĞƌŝĂůƐ ƐĐŝĞŶĐĞ ĂŶĚ ĞŶŐŝŶĞĞƌŝŶŐ͖ tŝůĞLJ͕EĞǁzŽƌŬ͕λσσς͘ ΀μ΁^<>E͘͞ŝĞŶĐŝĂĞ/ŶŐĞŶŝĞƌşĂĚĞůŽƐŵĂƚĞƌŝĂͲ ůĞƐ͘͟ĚŝƚŽƌŝĂůdŚŽŵƐŽŶ͘λσσς͘ ΀ν΁,^hd/ͳZE͘DD^ĂŶĚDŝĐƌŽƐLJƐƚĞŵƐ͗ĞƐŝŐŶ ĂŶĚDĂŶƵĨĂĐƚƵƌĞ ΀ξ΁ >:d/E zh͘ D͗͘ DĞƚĂůŽŐƌĂİĂ LJ dƌĂƚĂŵŝĞŶƚŽ dĠƌͲ ŵŝĐŽĚĞůŽƐŵĞƚĂůĞƐ͘ĚŝƚŽƌŝĂůD/Z͘^ĞŐƵŶĚĂĚŝĐŝſŶ͘ DŽƐĐƷ͘ ΀ο΁ZĞĐŽƉŝůĂĚŽĞůμνĚĞŵĂLJŽĚĞμκκοĚĞ͗ŚƩƉ͗ͬͬŚĞͲ ƌƌĂŵŝĞŶƚĂƐ͘ĞĚƵĐĂ͘ŵĂĚƌŝĚ͘ŽƌŐͬƚĂďůĂͬρŝƐŽƚŽƉŽƐͬĐƵρ͘ Śƚŵů

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