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  • Crystallographic Textures – Basics

    Dr. V. Subramanya Sarma

    Department of Metallurgical and Materials Engieneering

    Indian Institute of Technology Madras

    E-mail: [email protected]

  • OUTLINE

    • Introduction

    • Why texture is important

    • Classification of textures

    • How textures develop

    • Representation of textures

    • Measurement of textures

  • INTRODUCTION

    • Majority of engineering materials are polycrystalline

    • In latin, textor means weaver • In materials science, texture  way in which a material is woven

    • Each grain is a single crystal whose orientation differs from that of the neighbour

    • Many possibilities of arranging the individual crystallites

  • A fully textured sheet (Strong texture)

    A texture-less sheet (Random)

    INTRODUCTION

    Random Uni-axial or fibre Bi-axial

  • Texture influences the following properties:

    • Elastic modulus

    • Yield strength

    • Tensile ductility and strength

    • Formability

    • Fatigue strength

    • Fracture toughness

    • Stress corrosion cracking

    • Electric and magnetic properties

    ..........and many other properties.

    Why textures ?

  • Why textures ?

    • Properties depend on the texture present in the material

    • Tailoring texture to achieve desired properties

  • Textures can be classified as:

    • Macrotexture

    • Microtexture

    • Mesotexture

    CLASSIFICATION

    Macrotexture (Global / Bulk texture from volume)

    Can be correlated to the average properties of the material

    Determined by X-Ray, Neutron Diffraction

    Microtexture (spatially resolved texture)

    Determined by SEM/EBSD, TEM/SAD

    Mesotexture (relates to misorientaion / axis of boundaries)

  • CLASSIFICATION

    Grains marked with * have same orientation a) In a cluster b) Located randomly c) Have a different size compared to rest of the grains d) Are located in as special region i.e., surface

  • (i) Crystallisation / solidification (from a non-crystalline/liquid state)

    (ii) Plastic deformation (by glide or slip and twinning)

    (iii) Annealing (recrystallisation / grain growth )

    (iv) Phase transformation (due to orientation relationship)

    (v) Thin film growth (substrate orientation and strain energy)

    How textures develop

  • How textures develop

    Deformation textures

    • Constraint imposed during deformation causes lattice rotation

    • Under tension  increases and  decreases

  • How textures develop Deformation textures

    • Under compression  decreases and  increases

    • Rotation of the planes depends on stress state

  • How textures develop Annealing textures

    • Stored energy driving force for recrystallisation • Minimisation of interfacial energy driving force for grain growth

  • How textures develop

    Annealing textures

    • Grain boundary mobility related to the boundary character and precipitates / solute

    • Dissolution of precipitates could lead to abnormal grain growth

  • How textures develop Transformation textures

    • Texture in austenite will control the transformation texture in steel

    Bain Orientation relationship

    x y

  • • In order to specify an orientation, it is necessary to set up terms of reference, each of which is known as a coordinate system

    • Specimen coordinate system: Coordinate system chosen as the geometry of the sample

    • Crystal coordinate system: Coordinate system based on crystal orientation. In general [100], [010], [001] are adopted

    Textures representation

    There are two coordinate systems: •Sample (specimen) coordinate system •Crystal coordinate system

  • Textures representation

    Main mathematical parameters that are used to describe an orientation are:

    • Orientation matrix • Ideal orientation (Miller or Miller–Bravais indices) • Euler angles • Angle/axis of rotation • Rodrigues vector

    All these descriptors are employed to process and represent different aspects of macrotexture and microtexture measurements

  • • Orientation is defined as 'the position of the crystal coordinate system with respect to the specimen coordinate system',

    • where CC and CS are the crystal and specimen coordinate systems respectively and g is the orientation matrix

    • The fundamental means for expressing g is the rotation or orientation matrix

    Textures representation Orientation Matrix

    • The first row of the matrix is given by the cosines of the angles between the first crystal axis, [l00], and each of the three specimen axes, X, Y, Z, in turn

  • Textures representation Ideal Orientation

    A practical way to denote an orientation is via the Miller indices written as (hkl)[uvw] or {hkl}〈uvw〉

    Thus, rotation matrix g and Miller indices (hkl)[uvw] are related through

    In practice, the direction cosines from the orientation matrix are “idealized” to the nearest low-index Miller indices, for e.g. eg:

  • Textures representation Stereographic projection

    Stereographic projection is a graphical technique for representing the angular relationships between planes and directions in crystals in 2D

    – Can be used to calculate angles between planes etc. – Is used in the representation of orientation of crystals

    • We can represent the orientation of a plane using the normal to that plane

    • If we inscribe a sphere around the crystal of interest, the point(s) where the normal(s) intersect the sphere are the poles of the planes

    {100} poles of a cubic crystal

  • The projection of a plane (trace) passing through the origin of the crystal onto the surface of the sphere is a great circle

    • The projection of a plane that does not pass through the origin is a small circle

    • We can in principle measure the angle between two plane normals on the surface of the sphere to find the angle between two planes

    – We make this measurement along a great circle (MLK in figure)

    Textures representation Stereographic projection

    Great circles for the two marked planes

  • Textures representation Stereographic projection

    Making measurements on the surface of a sphere is tricky • Project everything from the spherical surface onto a plane – Pick a diameter of the sphere, put plane perpendicular to diameter and in contact with one end (or through the middle of the sphere), project from other end of diameter through entity to be projected onto the plane

    • As drawn, entities in hemisphere near B will end up outside the basic circle. Points on hemisphere including A will end up inside.

    – To avoid this problem, change projection point to the other end of diameter and distinguish points in the two hemispheres by marking them with different symbols (usually open versus filled in)

  • Textures representation Stereographic projection

    • Problems involving the stereographic projection are often handled using a Wulff net

    • Imagine a globe with lines of latitude and longitude marked on the surface.

    • Orient the globe so that the NS axis is parallel to the projection plane and project all the lines onto the plane

    • The longitude lines end up as great circles in the projection and the latitude lines as small circles

    • The lines in the projection can be used to read off angular coordinates

    • Just like using latitude and longitude to specify geographical location

    Wulff net

  • Textures representation Stereographic projection

    http://www.jcrystal.com/products/winwulff/

    • Projection from 3D to 2D

  • Stereographic projection

    Textures representation

  • Stereographic projection

    Textures representation

  • Stereographic projection

    Textures representation

  • Stereographic projection

    Textures representation

  • Textures representation Stereographic projection

    A standard projection shows the angular relationships

    between different poles for a given crystal orientation

    – Useful for identifying crystal orientations

    Standard projection

    Note all reflections on a common great circle belong to the same zone. The zone axis lies at 90° to the zone

    Standard projections for cubic crystals

  • Textures representation Stereographic projection

    Standard projections for hexagonal crystal for a given c/a

  • Textures representation Pole Figure

  • Textures representation Pole Figure

  • Textures representation Pole Figure

  • Textures representation Pole Figure

    {001}

    Plot (100) (111) (110) pole figures

  • Textures representation Pole Figure

    {100}

    Plot (100) (111) (110) pole figures

  • Textures representation Pole Figure

    {111}

    Plot (1