Single crystals have long range order and obviously they have short range order also. Such materials have well defined valence and conduction bands and a forbidden energy band as described by band theory of solids. Depending upon the band positions they can be metal, semiconductors or insulators. Now if short range order zero means long range order is also zero. This is a ideal disordered solid in which no electron can move , i.e., electronic conduction will be absent. This was proved theoretically by Anderson. For a very long time it was, therefore, considered that non- crystalline solids can not be semiconductors. in 1950s it was observed that chalcogenide glasses were semiconductors which had no long range order but had short range order.This is another situation of your question. Valence and conduction band do not have sharp cut of but have bandedges

Dear Dr. Sayyedan:

The idea of order in a conventional metallic alloys is very useful concept since depending on synthesis and processing of the alloy, distinct ordering level can be accessed giving a wide range physical and possibly chemical properties. Furthermore, a temperature of analysis should be specified.

If the discussion is restrict to solids type metal alloys, the concept of short or long order typically made use of one bond length as a qualitative measurement to describe the characteristic of the distribution or sometimes arrangement of a particular atom (hetero-atom) if homogeneous or not as a function of the distance of this hetero-atom or of these hetero-atoms with relation to a most common or most frequent atom of the alloy.

In this sense, metal alloy typically polycrystallines, a priori both type of orders occur the short range phenomenon occurs at interatomic distances, while long range ordering occurs at distances of thousands or billions of times an interatomic distances.

Unfortunately, there is a set of concepts coupled and further advances in its comprehension should be carried out with a careful procedure. In this way, it be possible to start with binary alloy system. From this point, there is a classic concept say that all solid solution is an alloy, but neither all alloy is a solid solution. In specific, the solid solution A:B or in broad sense AcB(1-c), being c = 0.5 gives a alloy with ratio 50:50 (equiatomic proportion between atomic species), in a bi-dimensional representation “2D” that is classical in papers and books, both atomic species exhibits a maximum real order represented by alternate atoms in any dimension, in fact three-dimensional lattice, 3D lattice. Here, seems that the short range order is an intrinsic concept, but the long-range order is connect with interactions between cationic species, see metallic bond nature, and symmetry. To think in symmetry is necessary have in mind the concept packing of atoms that is fundamental to understand the lattice relaxations phenomena and atom shifting under effects of temperature.

Further mechanistic modeling of the disordering in alloys has been carried out with investigation of the occupation of atom change site by site. In this sense, a parameter that allows a vision of the evolution of occupation of site by site along an alloy (binary) is the order parameter, which assumes values from zero to unity. A priori, values equal to zero represents represent a disordered state of a phase, while a value equal to 1 represents a fully ordered state of a phase; here is important to highlight that there is two states in a crystalline material are apprached. Further, analysis of these concepts can be found in literature from follow key- words, set of three key should be firstly tried: alloys, AuCu, ordered structures, tetragonal structures, “static concentration waves”, solids and structural transformations. See, above all concepts are correlated to crystalline state of matter satisfying some concepts as long range symmetry.

Also, there is amorphous (non-crystalline) alloy as an example some kind of poly-alloys and metallic glass with very particular properties engineered from extreme cooling rate. Here, specific cases should be investigated point to point. As a whole, I can be wrong, the order parameter ascribed to the long-range order in amorphous alloy seems more correctly described as being null (not zero) meaning none defined condition physically speaking. Then, the previous condiction given in the original question might indicate an exchange of symbolism.

Kind regards

Marcos Nobre

Short range order show the amorphous with some crystalline. Long range order show the polycrystalline.

Only for the chaotic systems one can talk about the complete disorder,  having no correlation between the positions of their  particles in space and time.  For this system you can't  even define any thermodynamics characteristic functions such as entropy and its conjugate variable  temperature!!

As far as the realistic solids and liquids are concerned, they have some sort of short range orders, which can be easily seen from the XRD radial distribution functions. The long range order  implies translational symmetry.  You might  have translational symmetry having the basis unit set,  which is composed atomic cluster or macro molecules well defined internal order or not.  In the case of metals and alloys having in the liquid states,  their coordination numbers don't change very much. There is no real amorphous state, which doesn' t have some sort of short range  in the sense of finite correlation time in regards to the positions of their first nearest neighbors. 

The measure of order may be   characterized by a  set of distribution functions   known as generalized functions,  which may represented by a well known quasi - Gaussian set which approaches  to  Dirac function as the limiting form. The width or the high of this generalized function may  be used as a metric to describe the order in numerically.   The same approach is also used in statistical mechanics without spelling the name of generalized functions. 

 I guess you are trying to say, What is the difference  between the average and local atomic structure. Is this correct ?

Hi!

For a long-range ordered system it is usually possible to define sublattices. Consider a B2 structure. One of the simple-cubic lattice type sublattices is occupied by A-type atoms, the other by B-type atoms. For perfect order and perfect stoichiometry you get a long-range order parameter equal to one. If, on the other hand, the two sublatteces are occupied by 50% A-type and 50% B-type atoms each, you get a long-range order parameter equal to zero. With a long-range order parameter equal to zero you can, however, still have short-range ordering. In the case here you would have a solid solution with bcc lattice. Consider a composition with 90% A-type atoms and 10% B-type atoms. You can not get a B2 structure with that. However, B-type atoms may still like to surround themselves with A-type atoms, while repelling B-type atoms in their neighborhood. So the average number of A-type nearest-neighbors for a B-type atom will be larger than the coordination number (number of nearest-neighbors) multiplied by 0.9 (the percentage of A-type atoms). This will lead to short-range order.

Hope this helps,

best,

markus

Dear Fatemeh,  From a naive point of view,  the short range order as far as its length scale is concerned it involves only the atomic rearrangements and their compositional redistribution  in the first and the second nearest neighbors. The most popular way of demonstrating  its existence is to use radial distribution function  4pi R^2 Rho(R) for each chemical species present in the alloy system. The XRD is the most powerful technique to be used for that purpose.  Also the resistivity measurements may be helpful to detect the existence of the short range order in partially ordered systems below the order disorder transition temperature. 

Long range order is closely related to the translation symmetry or the existence of the lattice structure where the individual atomic species occupies well defined positions in the primitive cell, which can be reached by well defined 3D  translation operations  every where in given matrix. According to this definition Long range order includes short range order but not visa versa.

Short range order is amorphous property itis meaning that the atom only connected with the nearest neighbours for example water steam but long range order is crystal characteristics in which the atome connect inthe intier materials and the atom form patternfor example diamond but non range order itis meaning the atom has no conduction band so the atom aren't connected with each other for example gas such as argon.