CLASSIFICATION OF BONDING IN SOLIDS:-

BONDS IN SOLID 


DEFINE:-

          A solid consists of billions of atoms closely packed and held together by strong mutual or interatomic forces of attraction.              The attraction and repulsion forces that tend to hold adjacent atoms at a certain spacing to keep the balance between the opposing forces are known as bonds. This process of holding the atoms together is known as atoms. These bonds between atoms make it possible for them to combine in a large mass to form a solid.


          The mechanical, physical, electrical and other properties of solids are influenced by the bonds. Therefore, different solids differ in their properties. 

          Bonds formed between atoms of solids are known as interatomic bonds because they are formed either by transfer of one or more electrons from one atom to another or by sharing of electrons between the atoms.


CLASSIFICATION OF BONDING IN SOLIDS:-


#Various types of bonds found in solids:_
(I) Ionic bond, 
(II) Covalent bond,
(III) Metallic bond, 
(IV) Van der waal &molecular bond


IONIC BOND:-
                        



Properties of ionic Bonding __

(a) Ionic bonds are generally crystalline in structure, in which ions of one type are surrounded by ions of other type in a systematic way. 
(b) These bonds are fair strong. 
(c) Due to high binding energies, the ionic crystals have high melting and boiling point. 
(d) Poor conductor of heat and electricity as compared to original metals. 
(e) Ionic crystals are highly soluble in ionizing solvents such as water and polar solvent like NH3. 
(f) They are transparent 

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Home rothery's rules and regulations (physics)

Hume-Rothery rules:-

HUME-ROTHERY'S RULES:- 

             In the course of an alloy development, it is frequently desirable to increase the strength of the alloy by adding a metal that will form a solid solution. In the choice of such alloying elements, a number of rules govern the for- mation of substitutional work of Hume-Rothery. Unfortunately, if an alloying element is chosen at random, intermediate phase instead of a solid solution. 

Hume-Rothery's Rules are described below. is likely to form an objectionable.

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CHEMICAL AFFINITY FACTOR 

             The greater the chemical affinity of two metals the more restricted is their solid solubility. When their chemical affinity is great, two metals tend to form an intermediate phase rather than a solid solution.

             Chemical Affinity Factor-The greater the chemical affinity of two metals, the more restricted is their solid solubility. When their chemical affinity is great, two metals tend to form an intermediate phase rather than a solid-solution. Generally, the farther apart the elements are in the periodic table, the greater is their chemical affinity.

RELATIVE VALENCY FACTOR 

              If the alloying element has a different valence from that of the base metal, the number of valence electrons per atom, called the electron ratio, will be changed by alloying. Crystal structures are more sensitive to a decrease in the electron ratio than to an increase. Therefore, a metal of high valence can dissolve only a small amount of lower valance metal, while the lower valence metal may have good solu- bility for a higher valence metal. 

              Relative Valence (Valency) Factor - It has been found that the metal of high valence can dissolve only a small amount of a lower valence metal, while the lower valence metal may have good solubility for the higher valence metal. For example in the Al-Ni alloy system both metals have FCC structure. The relative size factor is approximately 14%. However, Ni is lower n valence than Al and thus solid nickel dissolves 5% aluminium, but the higher valence Al dissolves only 0.04% Ni.

RELATIVE SIZE FACTOR 

            If the size of two metallic atoms (given approxima- tely by their constants) differs by less than 15 percent, the metals are said to have a favourable size factor for solid solution formation. So far as this factor is concerned, each of the metals will be able to dissolve apprecia- bly (to the order of l0%) in the other metal. If the size factor is greater than 15°, solid solution formation tends to be severely limited and is usually only a fraction of one percent.

               Relative Size Factor- If the two metals are to exhibit extensive solid solubility in each other, it is essential, that their atomic diameters shall be fairly similar, since atoms differing greatly in size cannot be accommodated readily in the same structure (as a substitutional solid solution) without producing excessive strain and corresponding instability. This is what referred as the term size factor. The extensive solid solubility is encountered only when the two different atoms differ in size by less than 15%, calleda favourable size factor (e.g. Cu-Ni, Au-Pt). If the relative size factor is between 8% and 15 % , the alloy system usually shows a minimum and if this is greater than 15 % , substitutional solid solution formation is very limited. 

LATTICE-TYPE FACTOR 

           Only metals that have the same type of lattice (FCC for example) can form a complete series of solid solutions. Also, for com- plete solid solubility, the size factor must usually be less than 8 percent. Copper-nickel and silver-gold-platinum are examples of binary and ter- nary systems exhibiting complete solid solubility.

              Crystal Structure Factor The crystal lattice structure of the two elements (metal) should be same (i.e. both should be of BCC, FCC, or HCP structure) for complete solubility, otherwise the two solutions would not merge into each other. Also for complete solid solubility the size must usually be less than 8%.

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Hume-Rothery's Rules are described below. is likely to form an objectionable.

रासायनिक प्रभाव क्षेत्र

             दो धातुओं का रासायनिक आत्मीयता जितना अधिक प्रतिबंधित है, उनकी ठोस घुलनशीलता है। जब उनकी रासायनिक आत्मीयता महान होती है, तो दो धातुएं एक ठोस समाधान के बजाय एक मध्यवर्ती चरण बनाती हैं।

रिश्ता वैधता का कारखाना

              यदि मिश्र धातु तत्व का आधार धातु से भिन्न भिन्नता है, तो प्रति परमाणुओं में वैलेंस इलेक्ट्रॉनों की संख्या, जिसे इलेक्ट्रॉन अनुपात कहा जाता है, को मिश्रधातु द्वारा बदल दिया जाएगा। वृद्धि की तुलना में क्रिस्टल संरचनाएं इलेक्ट्रॉन अनुपात में कमी के प्रति अधिक संवेदनशील हैं। इसलिए, उच्च वैलेंस की एक धातु केवल कम वैलेंस धातु को भंग कर सकती है, जबकि कम वैलेंस धातु में उच्च वैलेंस धातु के लिए अच्छा सॉल्यू-बाइट हो सकता है।

विश्वसनीय आकार फैक्टरी

            यदि दो धात्विक परमाणुओं का आकार (उनके स्थिरांक द्वारा अनुमानित रूप से दिया गया) 15 प्रतिशत से कम होता है, तो धातु को ठोस घोल बनाने के लिए अनुकूल आकार कारक कहा जाता है। जहाँ तक इस कारक का संबंध है, प्रत्येक धातु दूसरे धातु में apprecia- bly (l0% के क्रम में) को भंग करने में सक्षम होगी। यदि आकार का कारक 15 ° से अधिक है, तो ठोस समाधान गठन गंभीर रूप से सीमित हो जाता है और आमतौर पर केवल एक प्रतिशत का एक अंश होता है।

लेटिस-टाईप फैक्टर

           केवल धातुएँ जिनमें एक ही प्रकार की जाली होती है (उदाहरण के लिए FCC) ठोस समाधानों की एक पूरी श्रृंखला बना सकती है। इसके अलावा, कॉम-पिल सॉलिड सॉल्युबिलिटी के लिए, साइज फैक्टर आमतौर पर 8 प्रतिशत से कम होना चाहिए। कॉपर-निकेल और सिल्वर-गोल्ड-प्लैटिनम बाइनरी और टेर-नैरी सिस्टम के उदाहरण हैं जो पूर्ण ठोस घुलनशीलता प्रदर्शित करते हैं।

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Thermal stresses induced in bars of tapering section due to change in temperature_

Define Temperature Stresses :-


                 When ever there is some increase or decrease in temperature of a body, it cause the body to expand or contract. If the boys is allowed to expand or contract freely, with the rise or fall of the temperature, no stresses will be induced in the body. But if the deformation of the body is prevented some stresses are induced in the body. Such stresses are called thermal or temperature stresses.
                 The corresponding strains are called thermal & temperature strain.

                 Temperature stresses in beams or rods can be calculated as follows -
(i) Determine its expansion or contraction due to change in temperature assuming it is free to expand or contract.
(ii) Calculate the load required to bring the beam in original position.
(iii) Calculate stress and strain corresponding to this load.

 l = Original length of the beam
t1 = Initial temperature of the beam
t2 = Final temperature of the beam
 = Coefficient of linear expansion of beam material.
          (Elongation of the beam due to increase in temperature 
 If elongation of the beam is prevented by some external force or by fixing its end, temperature strain will produced in beam, which is given by,

                                

and temperature stress 




Q. A bar shown in fig. is subjected to axial forces and fixed at L and P. determine the forces in each portion of the bar and displacements of point M and N. Take  

         n
Sol     =>        

          Given,    




Forces in each portion 

   As we can see from figure, portion LM will be in tension, while portion NP will be in compression.
   The free body diagram of all three portion are shown in fig.
Now, for static equilibrium of the bar,

   
     R1+R2=100+50=150kN                       ........(1)
As bar is fixed at the ends, therefor extension of portion of portion LM will be equal to the compressions of MN & NP i.e,.
                                      

           

 

                 

                     

                   ............(2)

On solving equations (1)&(2), we get

 & 

Hence, forces in each portion,

      66.67 kN (tensile)                 

 

      

      

                 16.67 kN (compressive)              Ans

& 83.33 kN (compressive )              Ans

Displacement of point M,

 0.1587 mm    Ans

Displacement of point N,

here      

    Displacement of point N,

     0.1984 mm                    Ans

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Solidification of metals animation

Solidification of pure metals take place animation:-


                Solidification is the transformation of materials from the liquid the solid crystalline state on cooling.During solidification, the disordered structure of the liquid transforms to the orderly arrangement characteristic of the crystal. This process of solidification does not occur instantaneously. The process is characterized by the formation of numerous small particles of the new phase (s), which increase in size until the transformation completes. The process of solidification may be broken down into two stages-nucleation and grain growth. Nucleation involves the appearance of very small particles called nuclei, these nuclei then grow in size, untill the phase transformation is complete.

solidification of metals animation

            All solid metals are crystalline and crystals or grains are made up of several atoms. These individual crystals or grains are aggregated to form a visible mass of solid metal. These grains are formed when liquid metal solidifies. The process of solidification starts when liquid metal cooled below the equilibrium temperature (the temperature at which given metal exist simultaneously solid and liquid phase).
 Solidification starts when two or more atoms associate themselves to form very small crystal called nuclei. This may happen simultaneously at a Number of locations throughout the liquid metal. At these points a few atoms assume an orderly arrangement to give the unit cubic structure and growth takes place in three dimensional as shown in fig. As a result of this growth tree like crystals known as dendrites  [arise from Greek word dendrom  meaning tree ] are formed. A dendrite consists of unit cell, which are exceedingly small, first form in a straight line.




Slow rate of cooling promotes crystallization while a faster cooling rate of cooling rate may prevent crystallization. 

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Stress and strain. Hook's Law

DEFINE STRESS AND STRAIN:-

Stress-
             When some external forces are applied to a body, it offers resistance to these forces. The magnitude of this resisting force is numerically equal to the applied forces. This internal resisting force per unit area is called stress. Therefore, stress can be defined as the intensity of internal forces resisting change in the shape of the body. It is calculated by simply dividing on an area divided by the a: ea. It is measured in N/m2 o: kg the force acting cm2. There are three types of stresses namely, tension, compression and shear. Mathematically,
                                                               Stress, a = P/A
                                   where,             P= Force applied
                                                          A=Cross-sectional area.
[जब कुछ बाहरी बलों को एक निकाय पर लागू किया जाता है, तो यह इन बलों के लिए प्रतिरोध प्रदान करता है। इस प्रतिरोध बल का परिमाण संख्यात्मक रूप से लागू बलों के बराबर होता है। प्रति इकाई क्षेत्र के इस आंतरिक प्रतिरोध बल को तनाव कहा जाता है। इसलिए, तनाव को शरीर के आकार में परिवर्तन का विरोध करने वाली आंतरिक शक्तियों की तीव्रता के रूप में परिभाषित किया जा सकता है। इसकी गणना केवल a: ea द्वारा विभाजित क्षेत्र पर विभाजित करके की जाती है। यह एन / एम 2 ओ में मापा जाता है: बल एक्टिंग सेमी 2 किग्रा। तनाव, संपीड़न और कतरनी जैसे तीन प्रकार के तनाव हैं.]


Types of Stresses;-
                                 The various types of stresses may be classified as follows-

(1) Simple or direct stress 
(a) Tension               (b) Compression         (3) shear

(2) Indirect stress
(a) Bending              (2) Torsion

(3) Combined stress



Strain-
              Strain is defined as the deformation or change produced in the dimensions of a body due to the effect of stress on it. It is a ratio of the change in dimension to the original dimension. Mathematically
                                   
                               
                                             Strain,                                                                                                                                         

                where, 


 

  


          Strain is a dimensionless quantity. Depending upon the type of stress, it where, can be of three types, namely tensile, compressive and shearing strain.



Types of Strain ;-
                           The various types of strains may be classified as follows-

(1) Tensile strain
(2) Compressive strain
(3) Shear strain
(4) Volumetric strain.


Hook's Law;-

Define:

                      According to Hook's law, when a material is loaded within its elastic limit, the stress is proportional to strain, or in other words, within elastic limits the ratio of stress in a material to the strain produced remains. Mathematical


                                                           

                                                                     


                 Where,
                               E is a constant of proportionality, which is called as a modulus of elasticity, or young's modulus. It has unit as the stress, i. e. or






Poisson's ratio;-
                                       Whenever body is stressed within elastic limits, it is subjected to both longitudinal and lateral deformation. The ratio of the lateral strain to longitudinal strain is a constant quantity for a material and this ratio is known as Poisson's ratio. This ratio is designated by 1/m or u. Mathematically,

Poisson's ratio, 1/m or





Thus,  
           

The limitation of Poisson's ratio is that it can be applied only when material is stressed within the elastic limits

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