Determinación del número de bacterias Gram Negativas y Positivas

are thus related by

Kh(r) = K0(r) + k grad H(r) = K0(r) + h'(r)

This is equivalent to the Bragg relation Kh = K0 +h in the perfect crystal.

Insertion of the modified Blochwaves into the propagation equation leads essentially to the following fundamental results:

1. One can consider the presence of a local dispersion surface with the same equation as that associated with the perfect crystal case.

2. The existence of an amplitude ratio identical to that in the perfect crystal.

3. The knowledge that the Poynting vector associated with the wavefields is normal to the local dis­ persion surface.

It is also possible to calculate the trajectories of these modified Blochwaves using the Variational principle, and also amplitudes and intensities can be determined

after calculating the phase differences along the trajectory.

In the relatively simple case of a constant deformation gradient, (G = const, see appendix III) the trajectory

equation can be calculated analytically. These trajectories turn out to be the branches of hyperbolae ([169]).

The curvature of wavefields associated with branch

1 of the dispersion surface are of opposite sign to those associated with branch 2. This means that if both sets of wavefields reach the exit surface the resultant

intensity will not be very different to that corresponding to a perfect crystal. However if, as is the case as absorption increases, wavefields from one of the branches of the dispersion surface are damped out, contrast will result.

Under intermediate absorption conditions, and for a constant deformation gradient, when G is positive wavefields associated with branch 1 of the dispersion surface are curved in the same sense as the reflecting planes. The inverse is true for negative G.

A change in sign of G can be achieved by a change in sign of diffraction vector or vector displacement in the lattice. This means that Friedel's law is no longer satisfied (this is only valid in perfect crystals or non absorbing distorted crystals).

Fig. 50 shows the range of absorption conditions over which this can occur ([170]).

4

8

Fig 50 Illustration of the zones of black and white contrast as a function of deformation gradient and absorption (after [170]).

The upper and lower circles refer to positive and negative G

The kind of lattice deformation for the geometrical optics assumption to be valid was considered by Authier and Balibar ([171]).

Essentially G << 6, where 6 = rocking curve width, A = Pendellosung length, G = deformation gradient, or

These inequalities mean that the variation of the effective misorientation 6(A0) must be inferior to 5 over a Pendellosung length. They can also be expressed in terms of lattice curvature pL

Kato and Katagawa proved that the Eikonal theory is valid for B values less than 1 (of the order of a few tenths).

4.3 Essential Phenomena

4.3.1 Anomalous Transmission - Borrnann Effect ([172], [173])

values respectively

I

defining B as G = S p 5 « 1

or Blociiwaves propagating in a crystal. Each Blochwave is made up of a superposition of incident and diffracted components, EQ and EM respectively. Now for a particular wavefield the E0 and E^ components add together to give a travelling wave moving along the direction of the normal to the corresponding tie point on the dispersion surface (for the symmetric Laue case this is the bisector of K0 and Kh ), and a standing wave at right angles to this.

Anomalous transmission arises due to some of the wavefields having antinodes in between the atomic planes. Photoelectric absorption of an atom is proportional to the electric intensity there. This phenomenon is radically altered due to the presence of the standing waves so that those wavefields with antinodes in between the atomic planes will suffer less than normal absorption, and those with antinodes at the atomic planes suffer greater than normal absorption.

For Iron, a centrosymmetric crystal, the coefficient of Borrmann absorption in low order reflections only

differs from unity by the Debye Waller factor (see appendix III). A strong Borrmann effect can develop in these low order reflections, with wavefields from branch 1 of the dispersion surface experiencing absorption less than the normal photoelectric absorption.

4.3.2 Interbranch Scattering or Creation of New Wavefields This describes the transfer of energy which can

occur from a wavefield associated with one branch of the dispersion surface into another created wavefield which is associated with the other branch of the dispersion surface. This can occur when a wavefield encounters a planar fault, or when it -encounters highly distorted areas around, for example, a dislocation ([174], [175], [176] ) .

Although the Eikonal theory, can explain interference phenomena in mildly distorted regions, it cannot predict this creation of new wavefields.

4.3.3 Pendellosung Phenomena ([163])

Wavefields associated with branches 1 and 2 of the dispersion surface, whether they are defined from a plane or spherical wave viewpoint, interfere.

This interference can be described in terms of the Poynting vector of the energy flow within a crystal. For 1 reciprocal lattice point and two consequent tie points on the dispersion surface, the Poynting vector can be expressed as follows:

ST = [V#/e,]* <<S>> = SA + Sj + Sjj

This can be regarded as the vector sum of the effective Poynting's vectors of 3 wavefields in the crystal. Sj and

S2 are the effective energy flows each with its own

absorption, associated with a tie point on the branches 1

and 2 of the dispersion surface, respectively. S ia represents