This paper determines the orientational distribution of parmagnetic pigment crystallites on painted surfaces using EPR spectroscopy. The premise is that EPR could possibly reveal the application technique of the pigments. The authors did not find a strong effect for the pigment studied, since this particular pigment has crystallites with platelet morphology, which defeat the proposed method.

The work is of interest, although not of particularly high impact. It fits within the scope of Magn.Reson. Presentation quality is good, and referencing is decent. Data quality is good. The conclusions are partially supported by the presented data (see comments below). Publication in its current stage would be premature since the work has deficiencies in a few places, as listed below in no particular order.

1.

The discussion mentions that the crystallites are platelets. Authors should provide experimental evidence that the crystallites in their samples preparations are indeed platelets. There is a reference for this (Bloise, 2016), but the preparation procedure in that cited paper appears somewhat different.

2.

It is stated that the g-parallel axis is along the crystal c axis and that the c axis is normal to the platelet plane. Evidence for this should be presented, or cited, since it is essential for the interpretation of the data.

3.

In the discussion, it is hypothesized that the orientational distribution is affected by gravity and depends on whether the sample plane is horizontal or vertical during film drying. Only the horizontal case is shown experimentally. Why not the vertical? This would support the discussion that suggests that the platelets would then orient differently. Without experimental data on vertically dried samples, the discussion about the role of gravity is pure speculation and not useful.

4.

How are the 25x2-3 mm sample strips rotated around the axis perpendicular to the sample plane? This cannot simply be achieved by putting the sample strip into an EPR tube and rotating the EPR tube around its axis which is along the lab Y0 axis (Fig.3) in a standard EPR spectrometer. The experimental setup should be described in more detail.

5.

Were all samples dried with the application plane horizontal? This should be clarified in the Experimental section.

6.

To fully descibe the experimental setup, it is not sufficient to specify just the rotation axis relative to the sample (e.g, Z and Y in Fig.6), but rather (i) the orientation of the sample in the spectrometer (lab frame), and (ii) the rotation axis in the lab frame. Only then is the description complete.

7.

In general, it is more correct to refer to "random orientation distribution" as "uniform orientational distribution" or "isotropic orientational distribution". In analogy, a "non-random distribution" is better referred to as "non-uniform". This applies to several places in the manuscript.

8.

The reduction from the triple sum in Eq.(5) to the single sum in Eq.(6) should be shown mathematically, to improve clarity and rigor. In my understanding, one angle can be dropped because of the observed rotational symmetry of the EPR spectrum when the sample rotated around the Z axis. But what is the reason the second angle is dropped? The axial symmetry of the EPR spectrum?

9.

Eq.(3) is only approximately correct, since the transition probability depends on the g-factor along the microwave B1 field - for this, all three Euler angles are in principle needed. See e.g. the textbook by J.R.Pilbrow. The approximation inherent in Eq.(3) should be explicitly stated.

10.

Spectra simulations for the case in Fig.6(a) are missing from the SI.

11.

What is the reason the spectra in Fig.6a are more noisy than all the other experimental spectra presented in the paper?

12.

The lines in Fig.5(b) and Fig.10 are misleading, as they suggest non-zero contributions for odd l. I suggest to remove these lines and present the data in these figures as is done in Fig.8.

13.

In Figs. 8 and 10, the red dashed line should be removed. It suggests a continuous function, whereas the x axis is discrete. In this context, the tick marks in Fig.10 every 0.4 on the x axis make no sense.

14.

The left-hand side of Eq.(S3) is missing the omega(Omega') factor.

15.

What happened to the first integral in (S3)? Shouldn't there be an additional 2*pi factor for this integral appearing in (S5)?

16.

Figure S1 should include the simulation for all spectra in Fig. 4, not only a subset. Same applies to Figs. S2-S4.

17.

It should be stated somewhere that the odd-integer components of the orientational distribution give an EPR spectrum that appears isotropic. Therefore, as far as I understand it, odd l cannot be distinguished from l=0.

18.

- Line 113: matrice -> matrix

- The surname of the last author in the Hentschel reference is Spiess, not Speiss.

- The first line in SI section 2 should refer to Eq. S6, not Eq. S7.

- Eq.(S2) should say p_l and not p_{l00}, to be consistent with other equations.

- After Eq.(S2), it should say "determines an orientation Omega'" (prime is missing)

This paper is devoted to the investigation of preferential orientational distribution of crystallites of widely used copper(II) based pigment on painted surfaces using EPR spectroscopy. The underlying idea is  that the orientational distribution might depend on the way the pigment has been applied on the surface, and thus EPR might be used to reveal the application technique of the pigment. The conclusions reached by the authors is that in this particular case, given the specific combination of the morphology of the crystallites and its magnetic anisotropy the method cannot provide unambiguous response, while it might be of use for pigment with different morphology.

The work is performed accurately, and the results are, as whole, sound. The subject is of interest for Magn. Reason. Discussion, and is a nice tutorial on the effect of preferential orientation on EPR spectra. However I have a major point to raise as to the general applicability of the method. Indeed, while authors performed their measurements on samples prepared on purpose, the application of the proposed method on real samples would require detachment of part of  the painting to study. Does not this risk to be seen as a destructive method? A comment on this should be added in the Introduction.

A few minor points also require clarification and improvements before publication:

• Sample preparation: How were powders ground? Does the grinding procedure affect the spectra? Can authors provide an estimate of the size and anisotropy of the microcrystals they used (e.g. by the analysis of PXRD spectra)? I can imagine that the aspect ratio of the microcrystals can be modified by grinding, and this should result in different probability density as a function of the angle. This may have major consequences for the proposed method, and has to be considered. 
• Linewidth: can authors think of extracting some further information from the empirical depdence of the linewidth they extracted from the analysis of their spectra? Or, seen from a different point of view: is there a reason for the chosen functional dependence of the linewidth?
• It looks like the simulation of the spectra is much better when the orientational distribution is more isotropic: indeed, the simulated spectra for the sample magnetically oriented in fluid oil are much less convincing than the remaining ones. Authors should provide a rationale for this.
• The description of the different frames is somehow unclear: they state “the sample frame (X, Y,Z) with X, Y and Z axes having a defined position with respect to the sample.” If I got it correctly from Figure 3, they mean that the sample frame (X,Y,Z) define the orientation of the sample with respect to the laboratory reference frame. This has to be clarified.
• Did authors try to use larger magnetic field to orient the fluid dispersion? It appears to me that 20 mT is quite a low field, and higher fields should result in even more pronounced preferential orientation.
• The sentence “It must also be mentioned that during the film deposition and drying, the Z-axis is along the vertical direction so that the gravitational force is perpendicular to the sample plane” is a bit misleading: it is not a matter of the orientation of the Z axis (which is a choice of the authors), but rather of the fact that the gravitational force is perpendicular to the sample plane.
• Authors state that, in case of a vertical substrate, “gravity should tend to orient the plates perpendicular to the substrate”: it is however hard to see how this could happen, given the platelet form of the pigment. I can imagine an accumulation of the pigment on the low end of the substrate, but I cannot see why they should pile differently. A more detailed explanation of the reason for the expected effect should be given.