# Unit 1.9 – Crystal = Lattice + Motif

In this unit I want to come back

to the term crystal structure. This was already mentioned but

not explained in the last units. There is a simple formula –

a simple short form to memorize of what a crystal structure is. A crystal structure is a lattice plus the motif. The motif is sometimes

also called the base. So, we first have to look what lattice means, then what a motif is and in which

way it is linked to our crystals. A lattice is something mathematical

– it is defined as follows: A lattice is an infinite arrangement of points in space or in the plane or on a line, in which all points have the same surroundings. That means, a lattice in the plane looks like that: A genuine lattice would be infinite,

but that wouldn’t fit onto this slide. So just imagine that it is almost infinite. And now, we see that every single point

of the lattice has the same surroundings. That is true for this point with this neighbouring points in the

first, second, third sphere and so on. And this point has also the same surroundings. Now it should be also clear, why

a lattice has to be infinite according to its definition: Namely, because a point at the border does not

have the same surroundings as a point at the centre!

Therefore, there must be no border. Of course, in reality crystals have borders. And this leads to different physical or

chemical properties at their surface compared to the bulk phase. Now, we need the connection

to our crystal structure. What does such a lattice point represent? You can think of it as a connection

point between neighboring unit cells. This means, place a lattice point

at every corner of every unit cell. Here we have a piece of a crystal

with repeated unit cells that were joined together in

all three space directions. And now we place a lattice point at

every corner of these unit cells. And if we now look at the points only – for simplicity let’s take only two of the three

dimensions, namely the y,z-plane – then we see this lattice. And because our crystal consists

of an almost infinite number of unit cells our lattice can be

approximated as a real infinite lattice. A lattice is characterized by its lattice vectors. These are translational vectors; it is also sometimes said that

these vectors span the unit cell. And the lattice points can be transferred

into each other by these vectors, along the b-direction, along the c-direction, and of course the third dimension as well. Now only the motif is left. Our unit cells are not empty. They are filled with something –

and this is called the motif. The motif consists of the arrangement

of the building blocks of the unit cell. So this means normally some atoms, or a molecule. But, in principle, it could be

everything – like this car for instance. And the motif is represented by a lattice point. And if we apply this translational principle to this car we get this arrangement of cars, like a parking place. This parking place can be regarded as

a kind of a 2-dimensional crystal, if the cars are regularly arranged, and

if the cars are all of the same type. It is important that you understand that

the lattice is only a virtual construct, which describes the distance and the

direction from one motif to another. Okay, usually crystals are not made

by cars but by atoms or molecules. Let’s take, for instance, this three-atomic molecule – and let’s apply the translational principle – then we get this crystal. We see that the orange atoms are

translated by this orange lattice. And this must be also the case for the blue atoms. All building blocks of a crystal structure are subject to the same translational principle. Therefore also the green atoms

build the same lattice or are transferred to each

other by the same lattice. So, one can conclude that all lattices, which are built by the different atoms must be congruent, they are superimposable.

GreatFinally I had understand the meaning of motif even though I had taken crystallography course before more than a year!

Very very very useful courses. I watched all the chapters and they are very concise, interesting, and clear.

Hope you will make more tutorials!

one word: Marvellous

thnx so much sir…it is very helpful for me..now i am fully clear on this topic

Very good content, boring as hell though

I have a question about the notation to classify atomic chains inside crystaline structure. This is a notation with a letter C, a subscript number and superscript number and numbers between parentheses, as show in a paper from Arkhipov et al (2016) in Acta Crys E. I appreciate to much if ou can take a look about it. How this notation works?

so wonderfully explained sir…warm wish from me & if possible add some more topic on h.m symbol,detailed structure & minerallogy of mineral groups & desciption of minerals, economic minerals etc. that would be a great part to learn from you …

well explained sir

Nice explanation sir. I am having a problem in identifying motif in different crystal structure like Binary, ternary and others. For example in MoS2 and Mn2V2O7, Si2H2O3 there are different arrangements. In Mn2V2O7, Mn and V are not connected while in Si2H2O3, Si has H and O as neighbors. In such case how can we identify the motif? Can you please provide some suggestions.

Dear Frank (Sorry, you must be a lecturer but I don't know the proper title to call you by),

Thank you very much fro preparing and sharing these videos. I have been tasked to do research on materials science relating to solid state chemistry, but the basics I've learned about inorganic chemistry only taught concepts like symmetry (point groups, not space groups), closed-packed structures, vacancies and interstitial sites. So it was very difficult for me doing literature review because most sources expect me to have a basic understanding on crystallographic terms and analytical methods, of which I have no foundation on (I only knew Miller Indices and Schoenflies notation, but Wyckoff positions and space symmetry is totally alien to me).

Your videos personally make the field more approachable to me, and the short but concise explanation is excellent to make me get a gist of the concept and yet have initiative to want to find out more on my own to understand it (since now i have some idea of what to look for – asking the right questions can be difficult without knowing anything)

So once again, thank you. I am going to continue the rest for the series you have posted and hopefully be able to actually understand at least one literature of solid state materials without being confused even once

Best regards,

struggling postgraduate XD