The effect of applied field and temperature on SANS studies

Aside from observing the difference between the magnetic and nuclear Rg the po-

larised SANS study can also serve as a magnetometer tuned to the core magnetic moment. At q = 0 the intensity of the nuclear scattering is proportional to the scattering length of nickel (10.3 fm)200 and the intensity of the magnetic scattering is proportional to the magnetic moment on the scattering atom. Hence, from the ratio ofk1N uclear and k1 M agnetic, we can follow the magnetic properties of the core

species.

Figure 6.4 shows the effect of applied field on the ratio between the projected

Sq=0 for the magnetic and nuclear scattering channels at T = 300 K. During the

experiment the applied magnetic field was varied using an electromagnet - varying the current in order to vary the applied field. During the experiment the effective applied field was measured at the surface of the cryostat using a Hall probe/Gauss meter at various current settings (the result of which is plotted as the inset to figure 6.4 a)). The scattering ratio,S(0)Ratio = S_S(0)M agnetic_{(0)N uclear} shows a growth in the strength

of the magnetic channel as the applied field was increased, approaching 0 at the lowest applied field and ≈0.156(9) at high field.

As well as having aHdependence the crystallite magnetisation also identified a strongT dependence, however, at highHwe only assigned a Bloch’s law behaviour to the super-paramagnetic species.201 If we are not observing scattering from the outer layer of magnetic material it will not be included in theS(0) thermal behaviour. Figure 6.4 b) shows the effect of temperature on the S(0) ratio, fit by Bloch’s law

Figure 6.4: The effect of a) applied field, and b) temperature on the ratio of magnetic to nuclear scattering projected to q = 0 ˚A−1. Inset - current to magnetic field behaviour of the electromagnet utilised during the SANS measurements.

for low T spin waves,

M MS

= 1−αT32. (6.3)

The large error bars and the weak temperature dependence within this region makes it difficult to be certain about the temperature dependence and is reflected in a large error bar for the value of α = 2(1)×10−5 K−32, however, we do not see the same

Curie behaviour evident in magnetometry studies and the value of α is consistent with the value deduced earlier (1.02×10−5). The fit has a reasonable χ2_red = 1.33 and predicts theS(0)Ratio = 0.188(4).

As well as following the change in the ratio at S(0) each SANS measurement also provides values of the nuclear and magneticRg. Interestingly, the data shows no temperature dependence, suggesting that the previously reported thermal contrac- tion of metallic nanoparticles has no effect here,202;203and the data sets can be used together to give average values,Rg N uclear = 41.12(5) ˚A andRg M agnetic= 34.9(5) ˚A.

The magnetic neutron scattering length,bm, can be related to the size of the magnetic moment on the species, µ, by the equation

|bm| ≈γr0F(Q)|µ|, (6.4)

wherer0 is the electron radius (2.82×10−15m),γ is the gyromagnetic radius (≈2)

and F(q) is the magnetic form factor (F(0) = 1 and F(∞) = 0). If we assume that the nuclear Ni scattering has the same coherent scattering length as bulk Ni (10.3 fm) then the ratio S_S(0)M agnetic_{(0)N uclear} ≈0.548|µ|when the magnetisation is saturated. Using the value of S(0)ratio deduced from theH≈10 kOe data set this predicts an

average moment µ = 0.34(1) µB atom−1, a reduction compared to the bulk value

assumed of 0.61 µB atom−1. However, this value does not take into account the different scattering volumes (reflected by the difference inRg) which once corrected

for increases the average moment toµ= 0.58(4) µB atom−1much closer to the bulk

value of Ni.

6.3

Analysis of

N i

and

N i

scattering

Following the same procedure the nuclear and magnetic scattering have also been measured for theN iS and N iLsamples.

Figure 6.5: Typical 1D projections of the nuclear (red) and magnetic (orange) scat- tering for the N iS sample taken at T = 10 K, H ≈ 10 kOe. Both data sets have been fit by the Guinier-Porod model (black lines) with the best fit parameters given in table 6.2.

6.3.1 1D cross section analysis

Figure 6.5 shows the nuclear and magnetic scattering channels for the supported Ni catalyst N iS taken at T = 10 K and H ≈ 10 kOe. As with the previous sample the wide poly-dispersity of the samples means that the highq structure of the form factor has been smeared into a continuous Porod behaviour, so the Guinier-Porod approximation will have to be relied upon to evaluate the crystallite size.

The black lines on figure 6.5 represent the best fit to the Guinier-Porod model previously described with the associated parameters listed in table 6.2. The Guinier- Porod model gives a reasonable reproduction of the SANS data, with a χ2

red≈1 in

both cases, however, in order to achieve this the lowest q region of the magnetic scattering channel has had to be excluded from the fit.

The Guinier-Porod model implies a higher scattering count in the low q re- gion than has been measured, suggesting there are features which are excluded from

Parameter SN uclear SM agnetic Units Rg 39.66(4) 36.9(2) ˚A k1 3.460(8)×107 9.02(1)×106 counts cm−1 ∆Ω−1 k2 72.4(2) 17.6(4) counts cm−1 ∆Ω−1 ˚A4 y0 2.2(1)×104 −3.1(3)×104 counts cm−1 ∆Ω−1 χ2_red 1.14 1.61

Table 6.2: Best fit parameters of the Guinier-Porod model to the nuclear and mag- netic data of sample N iS shown in figure 6.5.

the Guinier approximation. Such a feature is possibly a result of inter-particle in- teractions (occurring at low q the feature needs to be associated with a long range scattering event) or a result of a core-shell structure. However, due to the high poly- dispersity of the sample this feature is too widely spread to be thoroughly understood in this study.

The radius of gyration values determined from the fitting show a slight re- duction in Rg N uclear compared to the N iH sample by ≈ 2 ˚A - less than is to be

expected from the previous gas adsorption and XRD peak broadening analysis. In- terestingly, the difference between the magnetic and nuclearRg terms has decreased

- mimicking the decreased shell magnetic contribution observed for the N iS sample

compared to the N iH sample during magnetometry investigations in chapter 5.3.1.