From this SEM photos I see the following:

1. Sample has cracks and very strong inhomogeneity in the composition, as well as macroscopically and microscopically. Cracks have arisen through the inhomogeneity.

2. Material, consisting of two components, was not sufficiently mixed: bright component (heavier elements: Y2O3-ZrO2?) was very poorly distributed.

3. Both mixed powders were quite fine-grained (heavy phase - nano powder, light phase - < 2 μm), but the powder of "heavy phase" was very strong agglomerated. During the mixing, these agglomerates were only partially destroyed.

4. Main component (gray phase, consisting of light elements: amorphous particle of silicates? SiO2?, SiO2-B2O3?, Al2O3-SiO2?...) remained amorphous after sintering and has about 50% porosity (black phase). Sintering temperature was not high enough for crystallization.

5. Particles of heavy and light components do not react with each other during sintering. Presumably, sintering temperature was too low.

6. Also for grain growth in remaining agglomerates of the heavy phase, sintering temperature was too low (< 1000°C?).

Thanks Vadim. What you are saying makes sense, especially the part about the crystallization failure, which explains why no grains are visible (because they are not present!). X-ray spectroscopy revealed that the white patches are indeed ZrO2.

The sample is a mixture of 70% Calcium Phosphate, and 15% each of Aluminium Oxide and Zirconium Dioxide. The sintering temperature and pressure were 1150 deg C and 80Mpa, low temperature is the reason for high porosity as you stated. 

Would you agree with my summary of your findings being that the Calcium Phosphate and Alumina have sufficiently bonded to form the gray phase (which is perhaps why you could not identify the third phase) and the white specks interspersed throughout the images are particles from the Zirconia agglomeration which have not reacted with the other two elements?

Dear Pretorius,

I would like to suggest you to use ImageJ program. Its free and you can assess the particle size or size distributions via "analyze particle" modulus. Also you can find lots of videos on Youtube about this issue.

Best Regards

Yes I agree with your summary.

Alumina and calcium phosphate have practically the same gray level in SEM, which is why they are difficult to distinguish, but smooth forms of pores and the whole gray phase indicates a dissolution of the alumina in phosphate melt. On the other hand, zirconium oxide was not dissolved in the phosphate melt (even the submicron particles of ZrO2 are readily visible in the middle of the melt). The explanation for this is a very low solubility of the ZrO2 in the phosphatic and silicatic melts.

Dear Tyron Pretorius

Have a nice day

I concur with Prof. Vadim Verlotski. Really, the images of your samples are very strange, they may be inhomogenous in their compositions and there are many cracks. This is may due to the mixing process is not done as it should be, as well as the grains distribution are very poor.

Therefore, I think that the data that can be obtained may not be accurate. 

Thanks

Dear Tyron, in line with what Fatih said, you could either use ImageJ, Global Lab Image (GLI) or Scion Image 4.03 for processing your images:

ImageJ: This software is available in http://imagej.nih.gov/ij/download.html. The version “ij149 1.6.0_24 (37MB)” works well in Windows XP and Windows 7, 8 and 10. Image J (freeware) allows performing on images the following operations in a pre-processing stage (i.e., a processing stage to convert the images into black & white images with less noise, prior to their final processing with Windows Paint/Photoshop/GIMP, first, and with GLI, second):

(with GIMP) Image > Mode > Gray scale (to convert to gray scale)

Process > Smooth

Process > Noise > De-speckle (to erase speckles?)

Process > Shadows …

Process > Enhance contrast (at 0.2% or 0.4% without equalizing the histogram)

Process > Binary > Make binary (to convert the image into black-and-white only, which is a mandatory step for GLI to be able to open the corresponding image)

Process > Binary > Dilate (optional)

Edit > Invert

Analyze > Analyze particles

Global Lab Image (GLI): This software is available in http://global-lab-image-2.software.informer.com/download/, http://image-processing-lab.software.informer.com/. GLI allows computing, for a micrograph or image conveniently pre-processed with Image J and Paint/Photoshop, a variety of parameters like number of grains, average dimensions, etc. Unfortunately, GLI does not work in Windows 7.  The uploaded images were 2592 pixels wide per 1936 pixels high, but GLI accepts images as large as (3000 pixels wide per 3000 pixels high). In any case, before opening the image with GLI, the user must define a buffer size in “File > New Buffer” identical to the size of the image (in pixels) to be opened, and the image must be Binary (pure black and pure white only; images can be made Binary with ImageJ). The button to click for computing grain size statistics is the one in the bottom right corner of the menu “Tools”. Remember always to perform the calibration. (see attached pdf for some details on GLI)

Scion Image: Another software useful for the processing of optical micrographs; it is available on-line but it is not for free: http://en.bio-soft.net/draw/ScionImage.html

Hope this is useful,

Jose

http://imagej.nih.gov/ij/download.html

http://global-lab-image-2.software.informer.com/download/, http://image-processing-lab.software.informer.com/

http://en.bio-soft.net/draw/ScionImage.html

Thanks a lot for all the answers guys, you've really cleared things up for me and set me in the right direction.

Dear Tyron Pretorius,

basically, the other contributors have said everything important already.

However, let me stress once again that a careful sample preparation is the basis for a qualitative analysis of the microstructure. 

Markus Engenhorst mentioned the method CSP (Cross section polishing) which I can warmly recommend - see an article of my PhD-Student below. 

The link is here: http://www.sciencedirect.com/science/article/pii/S0272884215016399

At the moment I do not have direct access to this journal myself. However, I could send you the submitted manuscript by E-mail.

With best regards

Torsten Staab

==============

Using a novel microstructure generator to calculate macroscopic properties of multi-phase non-oxide ceramics in comparison to experiments

By:Winkler, DER (Winkler, D. E. R.)[ 1 ] ; Staab, TEM (Staab, T. E. M.)[ 2 ] ; Muller, TM (Mueller, T. M.)[ 1 ] ; Raether, FG (Raether, F. G.)[ 1 ]

CERAMICS INTERNATIONAL Volume: 42 Issue:  Pages: 325-333

 Part: A

DOI: 10.1016/j.ceramint.2015.08.114

Published: JAN 2016

Abstract

A novel method to generate microstructures and calculate thermal and elastic properties in non-oxide ceramics, namely in Aluminum Nitride (ALN), Silicon Nitride (Si3N4), and Silicon Carbide (SiSiC) is presented. Structural features like dihedral angle (ALN), anisotropic material properties of grains (Si3N4), and multiscale structure (SiSiC) are considered. To ensure that the simulated structures are close to the real materials, several samples of all ceramics were prepared by the artifact-free method of cross section polishing and imaged by scanning electron microscopy (SEM). By image analysis chord lengths, phase fractions, connectivity between grains or elongation of grains were obtained. The same parameters were extracted from 2-dimensional sections of 3-dimensional representative volume elements produced by a structure generator. Structure generation followed closely the structure formation in the real process. It was repeated until close agreement between experimental and theoretical structures was obtained. Then, thermal and mechanical properties were calculated by finite element simulations. The calculated material properties showed good agreement to the obtained experimental data. (C) 2015 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

In a porous ceramic, the reliable way to measure grain is the use of optical microscopy

after proper etching and use appropriate magnification.

Pictures you got so far are not good enough for proper analysis. For sure you need to prepare new specimens as was advised above. Also:

1. Magnifications are too low. Of course you do need low magnifications, but for your structures you also have to obtain pictures with higher (much higher?) magnifications.

2. Accelerating voltage is too high (20 kV). You need to use lower voltages, at least 5 kV. High voltage "smooths" fine surface details and increase edge effect, making observation rather difficult. 

3. You have to try BSE detector. In many cases it can highlite phases of your specimen.

Grain boundaries are not so easy to see and to quantify dimensions of the grain size unless it is not etched. Etching enables bigger ditches instead of lines that separate grains on the micrography. Then also, porosity is making specimen more fragile to be polished to a flat surface and subsequently etched since that should be done by grinding with a send paper using specimen mounting in an epoxy resin. After that demounting and etching. Etching can be thermal, (where you change the system with another heating to a lower temperature), or a chemical etching which should be well determined with conditions of etchant type, concentration, and time of holding. The best etching solution is Ar ion beam etching, since it is uniform and less destructive for the specimen.

                Directly crystal structure cannot be declared from SEM images, although EDS Energy dispersive spectroscopy can lead to recognition of the phases due to either mapping of the elements specific for the compound, or from selected area approximately 1 square micron that is of interest.  But that is not crystal structure it is the presence of the elements on the behalf of which we can state the phase and possible crystal structure. Also EDS analysis give us proportion of the present elements indicating the phase and crystal structure.

                Your micrographs are made maximally by 5 000 times enlargement and that does not even indicate the grain boundary. But you have a distinguish parts that surely represent two different phases provisory visible as white and dark one. Dark phase is porous one, and white phase seems like agglomerated non sintered powder.

I will attach the publication regarding grain size and thermal etching