A single crystal is never a perfect single crystal as we define in crystallography and condensed matter physics. First of all it is not infinite according to its definition. However for a single crystal of say size of 1 mm there are about 10^22 atoms therefore can be considered to be of infinite size. But when you study its surface properties the finiteness is a defect because the atoms on the surface do not have translational symmetry and dangling bonds etc. There are often vacancies and extra (impurity) atoms in the spaces between atoms. The vacancies can trap electrons are form color centers which is another kind of interesting defects. These are defects of smaller size and are always present in a crystal. It is difficult to detect them but there presence can be inferred indirectly by several solid state property measurements. Now there also exist defects of larger sizes. Most important of these are dislocations. There are two types of dislocations: screw and edge dislocations. These defects can be photographed by microscopic techniques. The single crystal is never made of one piece of single crystals but constitute of domains which are slightly oriented from each other forming mosaic crystals. The mosaic crystals can be studied by X-ray diffraction through the effects of extinction. The domains in the crystal are formed below phase transitions. There can be large number of different types of domes depending the symmetry elements lost in the phase transition. The domains can be studied by diffraction and microscopy. The crystals can be twinned. These have been studied microscopically by crystallographers and mineralogists a long time ago. There are many other types of defects in a crystal and any standard book of solid state physics will give you introductory information. If you wish to go deeper then you must study specialized literature. There are several nice articles on defects in the Solid State Series (Academic Press) edited by Seitz and Turnbull.
In single crystals as obtained by the various available methods, we can observe the presence of isolated dislocations, subboundaries ... These defects can be observed by TEM, for instance. This is generally what we do to determine the quality of the produced single crystal.
A single crystal is never a perfect single crystal as we define in crystallography and condensed matter physics. First of all it is not infinite according to its definition. However for a single crystal of say size of 1 mm there are about 10^22 atoms therefore can be considered to be of infinite size. But when you study its surface properties the finiteness is a defect because the atoms on the surface do not have translational symmetry and dangling bonds etc. There are often vacancies and extra (impurity) atoms in the spaces between atoms. The vacancies can trap electrons are form color centers which is another kind of interesting defects. These are defects of smaller size and are always present in a crystal. It is difficult to detect them but there presence can be inferred indirectly by several solid state property measurements. Now there also exist defects of larger sizes. Most important of these are dislocations. There are two types of dislocations: screw and edge dislocations. These defects can be photographed by microscopic techniques. The single crystal is never made of one piece of single crystals but constitute of domains which are slightly oriented from each other forming mosaic crystals. The mosaic crystals can be studied by X-ray diffraction through the effects of extinction. The domains in the crystal are formed below phase transitions. There can be large number of different types of domes depending the symmetry elements lost in the phase transition. The domains can be studied by diffraction and microscopy. The crystals can be twinned. These have been studied microscopically by crystallographers and mineralogists a long time ago. There are many other types of defects in a crystal and any standard book of solid state physics will give you introductory information. If you wish to go deeper then you must study specialized literature. There are several nice articles on defects in the Solid State Series (Academic Press) edited by Seitz and Turnbull.
I forgot to mention that the presence of defects especially dislocations influence the hardness of the crystal. But it is not a easy job to infer much just from hardness measurements. Obviously for any definite conclusion you must also measure the harness of the same crystal without the presence of defects. Now it is not easy to find a crystal without the presence of defects.
X-ray diffraction line profile analysis may give some indirect information about dislocation density. I do not consider this to be a great technique. Microscopy is a much better direct technique.
Different spectroscopic methods like photoluminescence, cathodoluminescence, light absorption and others. But it depends on sort of solid. No metals of course.
Etching study is one of the prominent way to analyse the point defects and dislocations in single crystals. But, you have to find a proper etchant and optimise the etching condition to reveal the defects in the form of etch pits. The defect distribution can be studied by calculating the etch pit density in a crystal.
As Prof.Chatterji pointed out, the dislocation may influence the hardness of a crystal. But, from the hardness measurement, it is quite hard to analyse the type and density of the defects in a crystal.
For point defects the acoustic spectroscopy (solid internal friction) or the positron lifetime spectroscopy is the most sensitive detection methods.
BY using HRXRD is also an useful tool to measure the crystal perfection
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