define lattic , crystal and bassis
Answers
A lattice is a hypothetical regular and periodic arrangement of points in space. It is used to describe the structure of a crystal. Lets see how a two-dimensional lattice may look.
We have got the actual two-dimensional crystal in real space. So we may write:
lattice + basis = crystal
How do we define a lattice mathematically?
If r be the coordinates of a lattice point from any origin, then if we apply a lattice translation thought the lattice translation vector
\begin{eqnarray*}
{\mathbf {T}} & = & u{\mathbf {a}}+v{\mathbf {b}}+w{\mathbf {c}}
\end{eqnarray*}
then we would arrive at any other lattice point r$\scriptstyle \prime$ around which the environment would look exactly the same as around r.
\begin{eqnarray*}
\mathbf {r^{\prime}} & = & \mathbf {r} + \mathbf {T} \\
\; & = & \mathbf {r}+ u \mathbf {a} + v \mathbf {b} + w \mathbf {c}
\end{eqnarray*}
a, b and c are the primitive translation vectors or basis vectors which form the primitive cell of the lattice and u, v, w are integers.
Answer:
LATTICE : a structure consisting of strips of wood or metal crossed and fastened together with square or diamond-shaped spaces left between, used as a screen or fence or as a support for climbing plants.
Crystal : a piece of a homogeneous solid substance having a natural geometrically regular form with symmetrically arranged plane faces.
Basis : the underlying support or foundation for an idea, argument, or process.
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