One apparent randomness of the Zn-doped samples appeared as the distribution of the Néel temperatures (Fig.57). The spread of , which probably originates from inhomogeneity of the sample, may have smeared out the SR spectral structures, as discussed in the following.

We may suppose that the spread of was caused by an inhomogeneity of the
Zn concentration (*x*). Using the phase diagram shown in
Fig.53, the distribution of the Néel temperatures
() may be mapped to a fluctuation of the Zn
concentrations. The result yields and 0.5 % for the *x*=2, 4 and 8 % systems, respectively. These
variations of the Zn concentrations may be mapped to the spread of the
field-width using the inset of
Fig.57; the result becomes and 0.04 for the *x*=2, 4 and 8 %
samples, respectively. The above-mentioned spreads are all
Gaussian standard deviation.

The SR spectrum with the spread of internal fields can be obtained from a convolution:

In Fig.61, we show a simulated SR spectrum for the Zn 4% doped system (), obtained from a numerical integration of eq.60. The precession became less obvious than the Si-doped crystal; this result implies that the macroscopic sample inhomogeneity may be one of the reasons for the absence of muon spin precession in the Zn-doped systems.

The effects of more microscopic randomness, such as substitutions to the
spin site with the non-magnetic Zn ions, are not clear at the present stage.