Texture of Zircaloy components

1
Texture of Zircaloy components

• Texture is a measure of the Preferred
  orientation of the grains in a fabricated piece
  of the metal
• Two forms of anisotropy are required to produce
  texture
• - The crystal structure of the element must be
  anisotropic
• - The fabrication method must preferentially
  align a particular crystal axis with a
  macroscopic direction (e.g., radial in tubing,
  normal in plate)

2
X-ray diffraction
crystal axis
To interrogate a particular plane (or the crystal
axis direction ? to it), fix a combination of ?
and ? that satisfy the above condition
3
Stereographic projection

• source detector on surface of imaginary sphere
  of radius R locked at 2?
• specimen at center of sphere

• Bisector of 2? intersects sphere at P, defined
  by polar ? and azimuthal ?
• point P moved over hemisphere signal intensity
  recorded

Plate specimen

• if bisector happens to coincide with the normal
  to the plane with spacing d, an intense signal is
  recorded

• signal intensity is transferred to the
  stereographic projection plane (point P)
• when orientation resembles sl. 3, intense
  signals at ? 0 and ? ?

4
Stereographic projection diagram for Zry plate

• for Zry, called basal pole figure because ? is
  set to the spacing of the basal planes of
  the hcp crystal structure.

• the closed curves represent points of the same
  X-ray intensity

• the point PC is for ? 0
• PR is for ? 180o
• P is the projection of the maximum signal
  intensity at ? 40o

Avg intensity
½ of avg intensity

• virtually signal for ? 90o for ? gt 15o

• ? measured directly from projection
• how to determine ??

5
Determination of ? from the basal pole figure

• on ?(SPRPC), PCPR 2R (1)

• from ?(SPPC) tan? PCP/2R (2)

• from ?(SPV) tan? VP/VS (3)

• from ?(OPV)

VP Rsin? and (4) VO Rcos? (5)
VS R VO R Rcos? (6)

• insert VP from (4), VS from (6) into (3)

(7)

• insert (1) into (2) and the result (for tan?)
  into (7)

• measure PCP/PCPR from pole figure
• solve (8) for ?

(8)
6
Material properties anisotropy
(with respect to macroscopic axes)
Properties affected - thermal conductivity
- diffusion coefficients - yield strength

• Analysis of single crystallite
• thermal conductivities along crystal axes kltagt,
  kltbgt, kltcgt
• temperature gradient imposed along some
  macroscopic direction
• what is thermal conductivity in the direction
  (?,?) of ?

(these coordinate angles refer to any of the
macroscopic axes, not necessarily the plate
normal as in sl. 3)
7
Resolve heat fluxes along crystal axes
Add three contributions
In Zry, kltagt kltbgt so for the single crystal
8
Polycrystalline solid

• Want k in direction of plate normal (x see sl.3)
  so ? ? and ? ?

• must account for distribution of basal pole
  directions (i.e., ?) in plate

• measurement is the diffracted X-ray intensity,
  I(?,?)
• since the signal is not a function of ?, the
  intensity in a solid angle is denoted by I(?)
  (ignoring the factor of 2? from integrating over
  ?)
• I(?)d? ? number of basal poles in d? 2? sin?d?

• fraction of basal poles between ? and ? d?
  is

• thermal conductivity in the normal (x) direction
  of the plate is

9
Kearns factors
since sin2? 1 cos2?, the thermal conductivity
normal to the plate is
fx Kearns factor in the normal direction to the
plate
Also measure fy and fz for the transverse and
longitudinal directions
fx fy fz 1