Unit 1.3 – Definition of Crystals and Anisotropy


In this unit we will define the term crystal and will deduce first properties
arising from that defintion. Crystals – what does it mean? One way to approach an object is
to have a first look at the term – is it a foreign word? Does it mean something
in the other language? That is the case. The term “crystal” is Greek and means “ice”. Obviously, ice in form of
snowflakes or glaciers are crystals but of course there are other
crystalline materials that are not ice. The explanation is simply that ice
is used here in the figurative sense. Rock crystals can be found
very often and easily – here you see such a sample of Rock crystals, Rock crystals are a variety of Quartz, with a chemical composition of SiO2. And if you look at this picture you see that Rock crystals do not only look like a sort of ice but it was also thought in former times that these crystals were formed in extreme cold. In fact, the opposite is true as we now know. They are formed in great heat and under pressure. There are many, many varieties of
Quartz that can be found in nature – many are colored through the
inclusiuon of certain metal ions. Let’s have a look at a few of them: Firstly, the amethyst – it is a violet vareity of quartz and the colour is due to iron impurities
in connection with radiation of gamma-rays – here in a lovely, shiney brilliant cut. The milky quartz is colorless, there are no metal ions included, but here the inclusion of tiny liquid
droplets leads to this specific appearance. Finally, the Rose Quartz with its typical rose
color has another impurity included, namely a relatively rare mineral
of the class of silicates – – the Dumortierite. And there are many, many more. Apart from the circumstance what
the ancient Greeks had thought crystals have a clear defintion: Crystals are solid-state
bodies which are (a) homogeneous (b) anisotropic, and are (c) composed of constitutents that are
strictly 3-dimensional periodically ordered. This last attribute is the most important or the most prominent one. It is the very unique feature of this state of matter. There are of course other solid-state bodies, which do not show a perfect
order of their building blocks. This is true, for instance, for
wood, and plastic and glass… These materials are called amorphous. In general, this means, concerning
the aggregate states of matter we can divide these into: solid-state
matter, liquids and gases. And the solid state in turn can be subdivided into the two main categories amorphous and crystalline. In many textbooks on crystallography you can find relatively at the beginning
another defintion of crystals and that is: crystals have a crystal structure. This is actually not so helpful, iif one does not know exactly
what crystal structure means, however, I think with the given defintion here, we already have a kind of
intuition what could be meant and we will further elaborate this. What should be clear at this stage is that crystals are not something like that: Here a funny tiny animal is schematically shown. an ameba – a so-called change-animalcule, which can transform its shape
easily into something different. However, I do not know if it is able
to transform into something like that: a formation that resembles indeed in a way a crystal. Okey, what homogeneous means
should be immediately clear and we already have an imagination
what 3D ordering could mean, but what “anisotropic” means is probably not clear. Let me give you a first explanantion: All crystals show this feature called anisotropy. And this means that specific
properties of a crystalline material are different for different
directions – they are directional. The opposite would be isotropic, and means, in turn, whatever property you look at would be the same for all directions, for all orientations with respect
to an operation for instance. What kind of properties can be anisotropic? For instance: hardness and cleavability,
elasticity and expansion properties. Take for instance hardness: Anistropic hardness could mean,
that if you press a block like this from this direction it is very soft – but if you excert the same force from this side, the block is by far less soft. Other anistropic properties could be
electric or thermal conductivity, the electric polarizabilty and magnetization. In graphite, for instance, the electric conductivity is several orders of magnitude
higher along the graphene sheets running here horizontally in comparison to the conductivity perpendicular to these sheets. The understanding of such anistropic behaviors might be difficult for specific properties, in particular regarding the exact quantitative ratios. However, the origin of this behavior and the principle that lies behind it can be explained by a very simple picture: Look at this simple two-dimensional
assemble of spheres: it is periodically ordered as you will recognize. Now, we take two different directions and look at the sequence of the
spheres along these directions – the first one is this direction – we have here an alternating arrangement: There are two red spheres, one blue
sphere, two red spheres and so on. Aand these spheres are all lying
adjoined at the same line. Now, let’s take another direction – This one – here. The situatuon is obviously different. Now we have two red spheres, a blue one,
two red spheres and a blue one and so on. But: the pairs of red spheres are
oriented perpendicular to the blue ones – the blue ones lie in the indentation
that are created by these two red spheres, and if we now imagine that we want for example try to push the spheres along this or that direction it is quite clear that you have to exert different forces in order to move the spheres against each other. So, that’s it for now.

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