Gradients of Real Structure in Surface Layers

 

J. Drahokoupil1,2,*,M. Čerňanský1, N. Ganev2,  K. Kolařík2, Z. Pala2

 

1Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Praha 8, Czech Republic

2Faculty of Nuclear Sciences and Physical Engineering, Trojanova 13, 120 00 Praha 2, Czech Republic

jandrahokoupil@seznam.cz

 

Gradients of parameters of the real structure after surface machining have been studied by X-ray diffraction in steels. A surface is much more deformed than an inside, which may be without any modification. The parameters of the real structure, e.g., macroscopic residual stress, microstrain, and particle size have been studied. It is very useful to make measurements under various conditions (i.e., various angles j, y ;  more diffraction lines; several types of radiations). For describing radiation penetration depth into matter the term  “effective depth of penetration” can be used .  It can be computed, in case of  ω-diffractometer, as follow

,                                                                                                      (1)

where m(λ) - linear absorption coefficient, f(q,y) – function dependent on type of scan, θ - Bragg angle and ψ - tilt angle.

The mean value of some parameters which changes with depth is given by

 ,                                                                                                       (2)

where x (T)  = x0 + x1 T + x2 T2 + … (polynomial dependencies supposed); x – represents particle size D, microstrain e, or stress sij, and in some special cases x may also represent lattice parameter; h – thickness of specimen and  T – variable of depth.

The general least-squares analysis was used to obtain the parameters of the real structure. To study the residual macroscopic stress, the following general equation can be written as [1]

 ½[(cos2j +sin 2j +  sin2j) sin2y + cos2y +

        + (cos j +sin j) sin 2y ]+ (++).                                                         (3)

To determinate the particle size and the microstrain, the integral breadth was separated exactly as it is used in the single line Voigt function method [2]. Then the particle size and the microstrain may be obtained by:

,                                                               .                                             (4,5)

Where bc and bg are the Cauchy and Gaussin components of the integral breadth.

1.        U. Welzel, J. Ligot, P. Lamparter, A. C. Vermeulen and E. J. Mittemeijer, J. Appl. Cryst., 3, (2005), 1.

2.        Th. H. de Keijser, J. I. Langford, E. J. Mittemeijer and A. B. P. Vogels, J. Appl. Cryst., 15, (1982), 308.

 

Acknowledgements.

The research was supported by the Project № 101/05/2523 of the GA of the Czech Republic and by the Nat. Res. Projects AV0Z10100520, AV0Z10100522 of the Czech Republic.