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One sees vividly how the Pauli principle requires the collective state of the system to have a much greater minimal extension in phase-space. Indeed, for a system with N quantons not obeying the Pauli principle, the inequality 7 for the individual regions in phase-space applies as well to the total region, since nothing prevents the individual states to be one and the same.
It can easily be generalized to three or more… 3 dimensions. The reason of the discrepancy clearly is our neglect of the fermionic nature of the electrons.
The present derivation is both simpler and more transparent. The same reasoning may be applied to give a heuristic discussion of the all important question of the saturation of Coulombic forces in macroscopic matter namely, the constancy of the binding energy per particle with respects to the size of the system 8, shedding some light on the very sophisticated discussion by Dyson, Lenard, Lieb, and Thirring.
This type of argument also finds applications in the discussion of gravitationally bound systems, explaining the transition from rocks dominated by Coulomb cohesive forces to planets dominated by Newton cohesive forces , and even to white dwarfs9, This assessment does not fit well, to say the least, with the positive use of the Heisenberg inequalities in heuristic approaches as exemplified above , which, far from leading us to stumble against some alleged intrinsic limitations of our knowledge, enable us to gain some intuitive feeling of quantum phenomena More generally, the subtle, specific and constructive roles of h in many areas of modern quantum physics, should relegate the emphasis on a supposed quantum indeterminism to the historical record.
Once we fully accept quantum ideas, the whole terminology loses its meaning. Note that this criterion by no means is equivalent to setting up a distinction between microscopic and macroscopic quantities.
Indeed, he shows that a contradiction would appear if one were to apply the Heisenberg inequalities only in the microscopic world say, to the electron in a two-slit experiment and not in the macroscopic one say, to the screen in the same experiment. And we now know many macroscopic quantum effects, which make the point obvious see also below. From a modern point of view, it rather appears that this relationship in fact expresses the emergence of a new and original concept, which trancends both the classical concepts of energy and frequency.
This is the role generally played by universal contants, which may be best characterized as concept synthetizers Its role goes far beyond that of a simple unit conversion coefficient to which it is often unduly relegated; indeed, this very formula upholds the general concept of energy, surpassing the previously unrelated notions of work and heat. From that point of view, the relationship 16 is not to be interpreted as linking two classical concepts, but rather as transcending them through their synthesis, and establishing a new concept with a broader scope.
In fact, a new name could profitably have been given to this new concept, stressing its originality.
That the quantum energy thus constructed differs from the classical energy is sufficiently shown, for instance, by the fact that a quantum system is not, in general, characterized by a single and well-defined value of its energy, but rather by a whole numerical spectrum.
In other words, energy and frequency, through the relationship 16 appear as but two particular facets of a more general notion, each of which being the only visible one from either one of two specific viewpoints the wave and the particle aspects, respectively. Bunge probably being the best proposal A universal constant in general does not synthetizes a mere pair of notions, but unifies whole theoretical structures, and brings about several syntheses.
A further step may be taken, remembering the existence of yet another conserved quantity in classical physics, besides energy and momentum, namely angular momentum.
Now comes the bonus.
Indeed, contrarily to space and time, which are represented by the real line, angles define a compact set, the circle. This means that an angular period cannot be arbitrary, but has to be a submultiple of the full-turn daisies have an integral number of petals , i.
This line of reasoning may be extended to allow for half-integer values as well That the quantization of the angular momentum may be obtained from such a simple and deep argument clearly shows the interest of recognizing the nature of h as the universal quantum synthetizer. Far from being a mere convenience, this choice, exhibitng the identification of energy and frequency, entails the acknowledgement that there is but one single quantal notion of energy-frequency. It is only from a macroscopic and limited point of view that our dealing with objects approximately described as particles or waves has led us to set up two separate notions, energy and frequency, which we now recognize as particular aspects of a more general concept.
What I want to stress here is that there is more to it than a handy convention.
A time periodic phenomenon is specified by its period T. For a harmonic phenomenon, the most natural choice corresponds to a change of phase of the order of 1 radian — which is indeed a characteristic angle, neither too small a few degrees nor too large a full turn or so.
Despite the smallness of its numerical value in the SI unit system, many macroscopic phenomena, on the human scale, are governed by it. One of the tenets of the conventional view on quantum physics, put forward with considerable insistence by Bohr, is that all statements referring to the quantum world ought to be ultimately couched in classical language, in order to make sense with respect to our common experience.
It will be argued that such a requirement, although it certainly had a liberating effect on the emergence of quantum theory, can no longer be accepted at face value to-day. On the one hand, it is very difficult to see why this epistemological dogma, bearing on the overtaking of an old theory by a new one, should hold solely at the crossing of the frontier between classical and quantum physics, and not, for instance, when going from classical mechanics to classical field theory, or from galilean to einsteinian chronogeometry.
As for another contemporary bohrian view, namely, the correspondence principle, the argument can have but a heuristic and temporary value, its consistent enforcement being impossible — and counter-productive. On the other hand, more than half a century of quantum practice, both experimental and theoretical, has led to a new awareness of the quantum world and a genuine intuition of quantum behaviour, the expression, development and diffusion of which is seriously hampered by the lack of an adequate and specific terminology.
The delay in the emergence of a quantum vocabulary is to be contrasted with the rich and fruitful linguistic creativity of nineteenth century physics. Although it seems founded in theory on the Copenhagen position, this delay find its ultimate roots in the changes of scientific practice during the twentieth century specialization and separation of tasks.
It has had devastating effects on the conceptual understanding of quantum physics, both by physicists themselves and by philosophers, not to speak of laymen.
It is all the more necessary, if one wishes to reconcile quantum views of the world with contemporary culture, to exert a voluntary terminological activity, and to establish new ways of speaking for no-longer-so-new ways of thinking. Some proposals in this direction are discussed. It features a strange scene, where two physicists confront one another on some theoretical question.
This picture of theoretical physics as an aphasic knowledge entirely consisting of mathematical symbols, as common as it may be in popular representations, we know to be wrong, of course, and we have to acknowledge that, far from being mute, we are a very talkative kind; physics is made out of words. What I wish to question here, however, is the very nature of our relationship with language, particularly as concerns quantum theory.
My thesis will be that we have been somewhat offhand and rather indifferent with respect to the words we use, or rather without respect for them, and that this attitude has reinforced, and sometimes perhaps even produced some of the persisting epistemological and pedagogical difficulties in our field — not to speak of the new cultural problems that we are facing. Quantum physics and ordinary language It is obviously impossible to discuss this question without going back to Bohr and his famous argument on the use of language in quantum physics, which he stated again and again.
His position, as we all know, was that there is, and can be, no specific way of expressing quantum physics. The unambiguous interpretation of any measurement must be essentially framed in terms of the classical physical theories, and we may say that in this sense the language of Newton and Maxwell will remain the language of physicists for all time. If he refers to language in general, then his position is uncontroversial and verges on triviality; as a matter of fact, human language beyond the variety of specific languages is one, and there can indeed be no spoken or written communication outside of it, whether in physics or elesewhere.
The impossibility of creating ex nihilo a novel language, with syntactic structures previously unheard of, has nothing to do with quantum physics as such, and simply derives from the necessary continuity and commonality of all human experience.
Indeed, it has often been stressed that scientific language differs from ordinary speech mainly by the use of specialized nouns and adjectives, specific verbs being very rare and relating mainly to direct actions. One might certainly argue that science should not introduce any particular term and stick to the words of everyday language, in order to avoid creating a gap between common experience and scientific practice.
But the whole of science should then be rewritten anew, since right from it beginnings it has taken to create new words or coopt old ones in order to express its specific notions.
Bohr of course is quite aware that it is impossible to do science without using special words. In classical physics, this goal was secured by the circumstance that, apart from unessential conventions of terminology, the description is based on pictures and ideas embodied in common language, adapted to our orientation in daily- life events.
The exploration of new fields of physical experience has, however, revaled unsuspected limitations of such approach and has demanded a radical revision of the foundations for the unambiguous application of our most elementary concepts ….
It seems, however, very hard to justify setting up a boundary within science itself and to decree that it was all right to invent new terms up to, say, , but not afterwards.
In fact, the unintuitive character of the new physics, which is invoked by Bohr to justify sticking to classical terms, is by no means a specificity of the quantum domain.
In any case, beyond classical mechanics, the whole of nineteenth century physics has witnessed a continuous and manifold departure from the common understanding of the world.
In some sense then, the word preceded the idea and prepared its full extension; any forbidding pronouncement as to the introduction of non- archeo classical i. After Maxwell, they thought of physical reality as represented by continuous fields, not mechanically explicable ….
This change in the conception of reality is the most profound and the most fruitful that physics have experienced since Newton. But, as hinted at on the above examples, even technical terms are true words and carry a heavy load of historical connotations and conceptual associations.
It is no surprise, then, that these linguistic theories could not give full justice to the deep conceptual and terminological revolution witnessed by nineteenth century physics. The explanation is probably that an impending breakthrough is necessarily thought of as much more difficult that an already accomplished one — for those who do have to make the break. It has often been remarked that Bohr, a true Moses-like figure, did not really enter the Promised Land of quantum theory.
He used with an admirable dexterity the Principle of correspondence and the notion of complementarity to supplement classical physics with the lightest possible quantal touch able to open new vistas on the quantum domain9. One can then understand the deep heuristic role of his insistance on classical descriptions — and admire the extent of the results he obtained from such an a priori entrenched position. It is time to reaffirm that the creation of new words is a constitutive process of science, which should accompany the emergence of its new ideas, as it has done for most of the history of science — except during the century just ending, where linguistic inventivity has been drastically reduced, at least in physics mathematics and biology certainly fare much better in that respect.
Quantum physics and extraordinary language The past decades have seen a tremendous extension in our capacities for manipulating and exploiting quantum phenomena from the individual atomic scale single electron electronics, single atoms optics, nanotechnologies to the macroscopic lasers, superconductors, superfluids, etc. It is worth emphasizing that such feats not only were unforeseen by our great predecessors, but even declared unattainable in principle.
In any case, our growing familiarity with quantum phenomena has led us to a new intuition and, necessarily, to new ways of expression.
Any paper in the field is witness to this statement. Consider, for instance, the first page of a typical article, in which all nonclassical expressions have been underlined Fig. So, we do cultivate new flowers in our terminological garden. But my contention is that we do not take good care of it; by the way, I would not object to your interpreting this opinion as reflecting the old opposition between the apparently free growth of English gardens and the meticulously controlled planning of French ones.
Be that as it may, any amateur gardener knows that some upkeep is necessary, and that it consists as well in the weeding of obsolete vegetation as in the tending of young plants and in the sowing of new varieties.
However, we too often keep using uncritically such terms although they have lost most of their meaning. As already alluded to, this bohrian notion is but a sort of safe-conduct allowing a denizen of the classical domain to make some incursions into the quantum realm without running into trouble.
Deep inside this quantum realm, the conflicting classical views that complementarity is supposed to keep apart cease to hold altogether. It is certainly too simplistic to hope that a new reality can be fully described by the mere use, however ingenious, of previously conflicting ideas. Closely linked to the preceding argument, the description of quantum objects by a duality between two classical aspects is in fact of limited validity.
While it is a very useful point of view for the first contacts with these strange objects, it is by far not sufficient to take into account all the subtleties of their behaviour. Or, more precisely, what are the conditions of validity of these two exclusive but non complementary!
It is: You and in You It is: in your imparting the knowledge to the illiterates with faith and confidence It is: in your beneficial contribution to mankind with utmost care and sincerity.
Pillai is extremely grateful to the Honble President for his inspiring encouragement and abundant best wishes which helped Pillai to continue his academic activities with almost all perfectness even at this age. My greetings and best wishes to you and your family. Yours sincerely, A. Abdul Kalam This page intentionally left blank Preface xi Preface Materials Science is one of the subjects in which considerable advances have been made, both in theoretical understanding and in experimental work, over the last few decades.
To teach this subject for undergraduate students whose background is spotty, the major stumbling block proved to be the lack of suitable text books to supplement the lectures. Most of the available books, excellent though they are, rely heavily on the use of concepts completely alien to first or second year science and engineering students, and are largely aimed to cater the needs of post graduate students and research scholars.
The main book of the first author on Solid State Physics also belongs to the above said category. The author had the privilege of going through the recent changes introduced in the curriculum and syllabi of undergraduate courses in colleges affiliated to different universities spread all over the county.
The inclusion of the fascinating subject Materials Science as a core paper for the undergraduate courses in physics, chemistry, applied sciences, engineering and technology in recent years by a number of universities in India inspired Dr.
Pillai to bring out a small book in the present form and format to cater the present day needs, and thereby to improve the workaholic culture and also to enhance the grip of the undergraduate students whose background or pre-requisite in this vital area is not in abundance.
It is for this purpose this book is written. The first author reviewed the accumulated teaching materials prepared for his lecture classes over a period of 35 years. The second author strained in preparing the script in the form of questions and answers providing tables giving physical properties of materials at the end of each chapter. Inclusion of objective questions, problems with solutions under each chapter is the other salient feature of this book. The authors feel that the book now in your hands is handy; and they are prevalently hopeful that it will just serve the purpose.
Bonding in Solids 1. Some solids consist of molecules bound together by very weak forces. We shall not be concerned with these because their properties are essentially those of the molecules.
Nor shall we be much concerned with purely ionic solids alone bound by electrostatic forces between ions. The solids considered here are those in which all the atoms can be regarded as bound together.
To illustrate how the bonding is reflected in the properties of the solids, we explore the electronic properties of various types of solids. Solids display a wide variety of interesting and useful electronic properties. Good electronic conductivity is one of the characteristic properties of metals; semiconductors are the foundation of the Silicon revolution. But why is tin a metal, silicon a semiconductor and diamond an insulator?
Many solid state devices transistors, photocells, light emitting diodes LEDs , solid state lasers, solar cells are based on semiconductors containing carefully controlled amounts of impurity. How do these impurity affect the conductivity? These are some of the basic questions to be addressed; but a basic knowledge of bonding theory and the different mechanisms involved is absolutely essential to extend the study. What are the main causes and conditions for bond formation?
Answer: The forces which keep or hold together the atoms or molecules of a substance in the form of groups are called bonds. The atoms or molecules in the gaseous and liquid states are loosely-packed and a very little binding force exists among them. Therefore, gases and liquids do not possess any definite shape. If a gas or liquid is heated, it expands out indefinitely, showing that little binding force exists among its various atoms.
However, atoms and molecules in a solid are closely-packed and are held together by strong mutual forces of attraction. Therefore, solids have definite shape and occupy well defined space.
If a solid is heated, it does not change its shape easily, showing that a very big force exists that binds the various atoms and molecules. In other words the bonds in solids are very strong compared with that in gases and liquids. The law of nature is to make every system to attain a stable state by acquiring minimum potential energy. When two atoms come closer and unite to form molecules, their electrons rearrange themselves in such a way so as to form a stable state.
Inference The formation of bonds between atoms is mainly due to their tendency to attain minimum potential energy. When two atoms tend to form a bond, their valence electrons rearrange themselves so as to reach a stable state by acquiring minimum potential energy.
In the process, the two atoms lose some energy. The strength of the bond between two atoms would obviously depend upon the energy lost in the process.
Answer: The bond formed between two atoms by the total transfer of valence electrons from one atom to the other is called an ionic or electrovalent bond.