Effects of Diamond Crystal Imperfection on Coherent Bremsstrahlung G. L. Yang Department of Physics and Astronomy University of Glasgow

Contents 1. Crystal imperfection and possible effects of crystal imperfection on the coherent bremsstrahlung. 2. The diamond samples used in the present report. 3. Experimental results and analysis. 4. Conclusions.

1. Crystal imperfection Why a diamond crystal is imperfect? It is because any diamond crystal contains certain defects. The defects can be point, line, planar defects, inclusions or complicated clusters of impurity atoms. What will cause large amount of defects? Plastic deformation and radiation damage are two principle ways that are responsible for the generation of a large amount of defects. What crystal properties are affected? Mosaic spread and Debye-Waller factor

1.1 mosaic spread According to the mosaic model, an imperfect crystal is believed to be composed of large number of small mosaic blocks; within each block the distribution of atoms is perfect, but for different blocks, the crystal planes have different orientations. The angular spread of the mosaic blocks is usually called the Mosaic spread. A large mosaic spread means a poor crystal quality. Experimentally, we can estimate the value of the mosaic spread from the rocking curve width.

Effects of mosaic spread on coherent bremsstrahlung When the diamond crystal has a large mosaic spread, there is a variation in the direction of a given reciprocal lattice vector throughout the crystal, and hence the longitudinal component of the reciprocal lattice vector q l will be slightly different for different electrons. A different q l leads to a different x d, (the upper limit of the coherent peak ) and the averaged effect is that the edge of the coherent bremsstrahlung peak becomes broader

1.2 Debye Waller factor Thermal Debye Waller factor It decreases with increasing T (crystal temperature), and takes account of the thermal motion of the crystal atoms. Modified Debye Waller factor It takes account of the overall effect of thermal atomic motion and atomic disorder caused by defects. It will decrease with increasing defects number (N).

Effects of the Debye Waller factor on the coherent to incoherent ratio Debye Waller factor. When the Debye Waller factor decreases, and the Coherent to incoherent ratio decreases. I coh /I incoh

Least squares method Why introduce extra bacground? We can not directly measure the Debye Waller factor and the radiator temperature, both of which affect the coherent to incoherent ratio. How to introduce extra bacground? I me : measured data for diamond. I dt : theoretical data for diamond. I nt : theoretical data for nickel. How to get the best fit vary α and β to minimize X 2 to get the best fit. β/ α gives the value of the extra background

DBb :a nearly perfect diamond. Gwugr: a plastically deformed diamond. 2.Diamond samples used in the present report Radiation damaged diamond-Mainz

For Mainz diamond, no obvious difference of μ=β/α between the different x positions. For dBb, and Gwugr, differences in μ=β/α for different angles come from the experimental uncertainty. 3. Least squares simulation results

The variation of the width of the coherent edge of the Mainz diamond with x and z position. The x-axis is horizontal and the z-axis vertical, with the origin at the damage centre. When z=0.25 and 0.5mm, the x scan goes through the damaged region. Definition of the width of the coherent peak edge. Radiation damaged region Mainz diamond

Fig 6 Rocking curves at different positions along a line going through the radiation damage center. For a-h, each point has a distance from the damage center of: -0.75mm, -0.50mm, -0.25mm, -0.0mm, 0.25mm, 0.50mm, 0.75mm, 1.0mm arcseconds)

Relative intensity (I coh +I incoh )/I incoh of bremsstrahlung spectra for the Mainz diamond at different positions. The x-axis is horizontal and the z-axis vertical, with the origin at the damage center. It is shown that the Mainz diamond suffers from a macro stress, the crystal is possibly curved by this stress. The thinner the diamond, the more severe the effect.

4.Conclusions. It is found that an extra incoherent background is needed in order to optimize the fitting. Crystal defects and radiator temperature variations caused by electron beam heating do not have significant effects on the measured bremsstrahlung spectra. a diamond with a narrow rocking curve width has a sharper coherent bremsstrahlung peak edge than a diamond with a wide rocking curve width. A radiation damaged diamond shows evidence that it suffers from a macro stress which slightly deforms the diamond crystal, and causes a coherent peak shift.