Slides: Defectos cristalinos

DEFECTOS CRISTALINOS DEFECTOS CRISTALINOS •Adimensional (Point defects): Vacancies. Substitutional elements. Interstitial and self-interstitial atoms. •One-dimensional (Linear): Dislocations. •Two-dimensional (Surface defects): Grain boundaries. Rotation of small volumes leading to a polycrystalline aggregate. Stacking faults. ABCACABC Twins. Rotation and symmetry plane (…ABCACBABCBA…) Free surfaces and interfaces (catalysis, chemical reactions). •Volumetric (do not represent crystalline imperfections. Pores due to processing; cracks. •Transporte de masa •Aleaciones (soluciones sólidas) Arrhenius laws (1859-1927, Nobel Price laureate in 1903). Indicates thermally assisted processes. §Equilibrium Defect Concentration Varies With Temperature Boltzmann's constant ç ÷ ND N =exp -QD kT æ è ç ö ø ÷ No. of defects No. of potential defect sites. Activation energy Temperature Boltzmann's constant ç ÷ ND N =exp -QD kT æ è ç ö ø ÷ No. of defects No. of potential defect sites. Activation energy Temperature §k = • 1.38x10-23 J/at-K • 8.62x10-5 eV/at-K §N Todo lugar posible Energía de activación independiente de T No. of potential sites independiente de T Cómo encontrar la energía de activación para la formación de vacancias y autointersticiales? Forma logaritmica kT Q D D e N N- = ( ) ( ) T k Q NN D D1ln ÷ ø ö ç è æ -= En donde ( ) ( ) ( ) Tx kQm NNy mxy D D 1 ln where ® -®= ® = §La pendiente es negativa con lo que Qd es positiva 1/ T N ND ln 1 -QD/k slope Calculate the steady-state vacancy concentration in Copper at room temperature (25oC). ¿At what temperature would it be necessary to heat treat the material so that the vacancy concentration is 1000 times higher that that at RT? Assume that 20.000 cal are required to produce one mol of vacancies in Copper. Resolution: The lattice constant for Cu (FCC) is 0.36151 nm, so that the maximum number of vacancies per cm3is: Thermal effects on vacancy concentrations 3 22 38 atoms/cmcopper 1047.8 )cm106151.3( atoms/cell 4 ´= ´ =- n RT = 25 + 273 = 298 K: 22 3 83 exp cal 20,000 atoms mol 8.47 10 . exp cal cm 1.987 298K mol K 1.815 10 vacancies/cm NN RT Q n n æö =ç÷ èø æö - ç÷ æö =´ç÷ ç÷ èø ç÷ ´ - èø =´ Temperature to increase a 1000 times this concentration: 11 22 o 1.815 10 exp (8.47 10 )exp( 20,000 /(1.987 )), 102 C Q NN RT TT n n æö =´=ç÷ èø =´- ´= FCC BCC •Fe has FCC structure at high temperature whereas it has the BCC structure at lower temperatures (i.e., RT). Transformation occurs at 910 ºC. 1.5 1.5 3 1 2 per face x 6 faces = 12 1 2 •In FCC Fe, carbon occupies octahedral interstices. •In BCC Fe, carbon also occupies the octahedral interstices!! •12 tetrahedral interstices en BCCs and 8 tetrahedral interstices in FCCs. •4 octahedral interstices in FCCs and 6 octahedral interstices in BCCs. •Greater solibility for C in Fe for the FCC than for the BCC structure. •Anisotropic displacement of carbon atoms in BCC Fe. i f x (c) 2003 Brooks/Cole Publishing / Thomson Learning Figure 4.4 the perfect crystal (a) is cut and sheared one atom spacing, (b) and (c). The line along which shearing occurs is a screw dislocation. A Burgers vector bis required to close a loop of equal atom spacings around the screw dislocation. Dislocación de tornillo (screw dislocation) x i f !"ℎ$%&'( )ℎ*+,&ℎ+,) )ℎ' -.(/+"$).+% /.%', 1*'2$.%( "+%()$%) )ℎ*+,&ℎ+,) )ℎ' '%).*' /++3 Edge: Screw: Dislocaciones… Mixed dislocations bis preserved throughout the loop Superficie libre Superficie libre ! ! ! ! ! ! ! Dislocation glide occurs in the highest packed {111} plane in FCCs. Glide direction is of the compact <011> type in FCCs. b ξ ; screw dislocation b ξ; edge dislocation ! " # $ = 0 = '()* ! × # $ = 0 $Always unit vector Vector AD = [10-1]. Con lo que un vector unitario en la dirección de bserá Con lo que Si el vector de Burgers tiene una magnitud que es justamente (√2 a)/2 ; obtendremos entonces que Un sistema de deslizamiento que incluya a este vector será aquel que contiene un plano de mayor compacidad de normal ntal que n!b= 0. Por inspección, por ejemplo, n= (-11-1) 0 (111). c •BCCs: Multiple parallel {112] planes and thickening along the <111>. •FCCs: Multiple parallel {111] planes and thickening along the <112>. Maclas (twins) Intercaras y bordes de grano (de superficie) Intercaras y bordes de grano Interfaces and grain boundaries Read-Shockley Model tgq=b/d Energía per unit area g = s = Energdislocación * 1/d Energía per unit area g= s ~E b2* 1/d = b tg q E (q) plateau= 500-1000 mJ/m2 Interfaces and grain boundaries (microstructure) •Si la interface tiene mayor coherencia (valor de gbajo) entonces tenderá aser naturalmente inmóvil mientras que la mobilidad aumentará con la incoherencia;es decir para energías gelevadas.En este caso, los saltos atómicos de un lado de la interfase pueden ser incorporados en el otro debido a la cantidad de espacio libre en la interfase. Coherent and incoherent twins Lower energy! Interfaces and grain boundaries (microstructure)