Dear O. F. Farhat

Peace be upon you

Noting that the intensity of the diffraction lines depend on the growing process as well as the deposition conditions and in the same time they dependent also the degree of crystallinity of deposited sample. I think that in your case your crystallites were arranged in the plane xz, i.e. they prefer to grow in the plane (201) and are not formed vertically (002) (not perpendicular to the substrate). It worthy to mention also that the broadening of the obtained beaks are dependent upon the strain.

Good luck

Dear colleague O. F. Farhat,

Have a nice time and good day.

The increasing of the intensity of XRD is always accompanied by the decreasing of the full width half maximum, FWHM. Such this issue supports the increasing and the enhancement of material's crystallization or the order of the material. Your obtained data confirm that the order of your material through the preferred orientation of (201) is more than the order of the preferred orientation (002). The conclusion of that the crystallite size through the preferred orientation (201) will be larger that through the preferred orientation (002). To confirm this assumption, you can use the well know "Sherrer equation" to calculate the crystallite size through the two obtained preferred orientations (201) and (002). All what you need the value of FWHM which you can calculated by origin lab. software. the attache paper teach you how to calculate the crystallite size using "Sherrer equation" and other techniques. If you study your sample using transmission electron microscope, TEM you will see and confirm the crystallite size and the XRD data.

I wish this help you and be useful.

Yours

A. EL-Denglawey

Dear O.F. Farhat, please consider first that (hkl) are used for lattice planes whereas hkl are Laue indices for a description of a reciprocal lattice point which can be assigned to a interference intensity. Therefore you can use (201) but then it is a lattice plane. 201 describes the respective first order interference of (201). For (002) it is more dramatic since (002) does not exist at all. It has to pass lattice points but you can try it. For the respective distance d_(hkl) no lattice points exist (for a P lattice which is the case here). Therefore, correct would be: 002 as second order interference of (001). Miller indices are defined as prime to each other. This makes writing easier since you don't have to write always lattice plane (001) or interference 002. It is automatically expressed. It prevents a lot of irritations and misunderstandings if we use the correct writing. You also cannot say, the distance is 2 since you don't know the unit. In so far, the correct application of (), {}, [] , ::...are the units for planes, directions, vectors in crystallography, cf. International Tables for Crystallography. Unfortunately you are not the only one who does not care about it...

If you are talking about ZnO, you hopefully mean the hexagonal modification? Or are you talking about the cubic? This is often a very important information since both are different. Nevertheless, the major statement is independent. I only tried to check it, how much is the difference between both interference intensities. Sometimes it may happen that a wrong input file (structure description) has some errors and we are talking about something non-existing.

If you simulate and XRD pattern the major assumption is that all crystal orientations have the same probability. The biggest deviation is a single crystal. In this case you will only measure in Bragg-Brentano geometry the interference of the plane which normal is exactly in between ingoing and "outcoming" beam. Often this is even impossible because you need to align the crystal very accurately and therefore used as ideal sample holder for a powder since then no signal comes from the sample holder (people use Si single crystals slightly misaligned). This arrangement of incoming and outgoing beam is often misunderstandingly interpreted as reflection (which is physically wrong but simple to explain during a lecture or explaining Braggs law).  You can imagine that a usual sample is somehow in between: never shows an ideal orientation distribution of grains of the same size, but only rarely it will be single crystalline (then you know it, or the crystals are too big). However, this distribution affects the intensity of each interference. It can be zero or shows the expected intensity. For powders one has to take into account that  for each theta angle different crystals contribute to your diffractogram. This is also not always clear but has to kept in mind. If you want measure another interference for this specific "reflection" condition, the respective plane has to be parallel to the surface (or more accurately: the normal is exactly between primary beam and detection direction, above written as ingoing and "outcoming" beam). There are also some other effects like the application of variable slit, the geometry used, the radiation used etc. and not only the structure factor given by the phase observed.  These influences are often combined to the LPG factor (Lorentz, polarisation and geometry factor) which dramatically affects the intensity ratio. However, if the geometry used is known, all calculated intensities can be corrected considering the related effects. 

Why you observe (201) instead of (001) as strongest interference can have different reasons, e.g. the above mentioned crystallization process applied, or simply for crystallographic reasons, i.e. the crystal structure or lattice matching to the substrate.

The above mentioned anisotropic peak broadening is an additional explanation but not often observed. However, it should be anyway clear that not the hight of an interference describes the intensity, but the area below the peak. This means, even  for a homogeneous orientation distribution you can observe narrow high but also lower and broader peaks. If you observe such cases it indicates that crystals are not well described by a spherical shape (what is a commonly not well matching assumption but still used since often it is acceptable matching) but by plates or rods with a strong form factor quite different from 1.

Finally we can say that there are many reasons for such an effect, but to discuss it seriously you need to post the diffractogram in order to evaluate about what you are talking, peak hight or peak area, texture effects, particle size effect, strain etc. All this you can find much better and more systematically explained in mainly older books like Klug-Alexander were the fundamentals are often better explained and not only the recent developments in data processing. You can have the best data processing but it is useless if your data are of bad quality since you do not understand the very fundamental things which are preassumed in these software packages. If the experimental data do not match these assumptions any analysis with the best software is actually useless and will generate wrong results.

i agree with all these answer, but according to my opinion, the answer may correspond to lower form factor corresponding to that plane. it is not necessary that every plane contains equal Zn atoms.

Best regards, A. Ahad

@ A. Ahad, here you perhaps don't understand the concept of lattice planes. Every plane consists of lattice points, and every lattice point represents the same number of Zn and O atoms given by the stochiometry. Only the number of lattice point changes with hkl and depends on the d_hkl since the lattice point density is constant (number per unite cell). If d_hkl is half that big the number of lattice points is also half that big since you have to "derive" them on more lattice planes.

You perhaps mean atomic layers, but this has nothing to do with lattice planes!   

U need to be more spesific because ZnO has a few phases; if hexagonal than it's caused by preferred orientation, but if cubic (Pm-3m) than no need to explain.

The attached picture shows a preferred orientation of ZnO crystal (yellow marker).

Hope you get some idea here, http://instanano.com/characterization/experimental/uv-vis-xrd-infrared-ir-raman-zinc-oxide-zno/