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To experimentally investigate the disorder and quality of the sample, powder X-ray Diffraction (XRD) was used to study the crystal structure and disorder of the sample. XRD was performed using Cu Kα radiation (∼ 1.5418 ˚A) from an angle 2θ of 25◦ to 125◦ for a duration of 24 hours. Cu Kα was used due to the heavy Co fluorescence created when using a Mo source.

An initial Rietveld refinement129 was performed using the GSAS130,131 code. The lat-

tice parameter was determined to be 5.652±0.001 ˚A, in very good agreement with the literature and theoretical calculations. The model found no improvement when disorder was taken into account contributing to the evidence that the sample was stoichiomet- ric. The Rietveld refinement has been plotted in figure 6.13. In general, the Rietveld

30 40 50 60 70 80 90 100 110 120 0 1000 2000 3000 4000 5000 I n t e n s i t y [ a r b . ] 2 [°] Powder XRD GSAS Model Background Residual

Figure 6.13: XRD diffractogram captured for Co2MnSi powder using Cu Kα1 and Cu

Kα2 X-ray radiation.

Site X sites Y sites Z sites

Co 2−γ−β γ β

Mn γ 1−α+γ α

Si β α 1−α−β

Table 6.1: Definition of the number of constituent atoms in Co2MnSi, related to the

disorder parameters α,β and γ.

sities are underestimated for the [440] and [620] reflections. Unfortunately, due to the energy of CuKα radiation, the Co in the compound fluoresces, reducing the XRD signal significantly. This can cause quite a considerable change to the measured intensities of the XRD peaks. As a result, while the measured reflections are counted at their ap- propriate angles, the intensities may not be believable due to issues with the measured background.

Takamura et al.132 devised a different means of measuring the atomic disorder of full- Heusler materials as demonstrated by their analysis of the disorder in Co2FeSi thin films.

This new technique involves using Powder XRD with a CuKαand CoKα source. While the different sources will shift the scattered peaks in 2θ due to their energy differences, another difference arises due to the X-ray anomalous scattering from the two sources.133 Quantitatively determining the on-site disorder for the full-Heusler is expressed using three disorder parametersα,β andγ and determined from a physical model proposed by Niculescu et al.134 Here, α represents the the exchange between the Mn and Si atoms,

β represents the exchange between the Co and Si atoms, andγ represents the exchange between the Co and Mn atoms. Once the disorder parameters have been determined, calculating the composition of Co2MnSi can be performed by referring to table 6.1. In

order to determine these disorder parameters, the peak intensities of the (111), (002) and (220) reflections from the XRD data need to be determined, for these can then be related to the atomic scattering factors of the Co, Mn and Si. Figure 6.14 plots the calculated atomic scattering factors for both the Cu Kα and CoKα sources.135 Here, the atomic scattering factors for each element have been plotted as a function ofsinθ/λ, whereθ is the scattering angle and λis the incident X-ray wavelength.

0.15 0.20 0.25 0.30 8 10 12 14 16 18 20 22 A t o m i c S c a t t e r i n g F a c t o r | f | sin ( ) / [ Å] Co Mn Si ( 1 1 1 ) ( 0 0 2 ) ( 2 2 0 ) CuKα Source 0.15 0.20 0.25 0.30 8 10 12 14 16 18 20 22 ( 2 2 0 ) ( 1 1 1 ) A t o m i c S c a t t e r i n g F a c t o r | f | sin ( ) / [ Å] Co Mn Si ( 0 0 2 ) CoKα Source

Figure 6.14: Calculated atomic scattering factors for Co, Mn and Si from Cu Kα and CoKα sources.

intensity of the (220) reflection. The crystal structure factor83 for the (220) direction

F2202 is related to the atomic scattering factors by

F220 ∝2fCo+fMn+fSi (6.7)

wherefCo,fMn and fSiare the atomic scattering factors of Co, Mn and Si respectively.

After the datasets have been normalised, the (111) and (002) reflections can be used to determineα,β andγ using the following two simultaneous equations:

F111∝(1−2α−β)(fMn−fSi) + (γ−β)(fCo−fFe) (6.8)

F002∝(1−2β)(fCo−fSi) + (1−2γ)(fCo−fFe). (6.9)

The collected Co Kα source data is plotted with the Cu Kα source data in figure 6.15. This style of analysis, where the peak intensities of two different datasets are compared

30 40 50 60 0 2000 4000 6000 8000 10000 12000 ( 2 2 0 ) ( 0 0 2 ) Co source I n t e n s i t y [ a r b . ] 2 [ °] ( 1 1 1 ) ( 1 1 1 ) ( 0 0 2 ) ( 2 2 0 ) 30 40 50 0 2000 4000 6000 8000 10000 12000 Cu source 2 [ °]

Figure 6.15: Measured XRD patterns for CoKα and CuKα X-ray sources.

2

is heavily dependent on a high signal to noise ratio. The values forα,βandγ were found to be 0.081, 0.007 and 0.513, respectively. These values suggest a significant amount of disorder between the Co and Mn atoms with a small disorder between the Mn and Si and a negligible disorder between the Co and Si. When considering the success of the theoretical work combined with the 5 µB total moment measured using the SQuID,

and EDX work which suggested a small disorder between the Co and Si sites, it is not feasible for the sample to possess this level of disorder between the Co and Mn sites. For further analysis of the disorder to continue, a higher quality data set for the Co source needs to be measured.