I had performed a Vicker's Harndness test on the two specimens of Cu and Al respectively .Despite the fact that both of them have the same stucture. How does the hardness vary so much?Please explain with proper reasons to context.
It appears that you are seeking a correlation between hardness and the crystal structure of a material. Unfortunately, such a direct correlation does not exist.
To understand this in detail, it is important to revisit some definitions:
Hardness is the resistance to plastic deformation and is highly dependent on the dislocation mobility of the material.
What you might be more interested in is the Elastic Modulus, which is the measure of the stiffness of a material.
Elastic modulus depends on the absolute value of the bond length and the bond energy (this is the resistance to bond stretching). Although Al and Cu have the same crystal structure, their bond lengths and bond strengths are very different. Hence their modulus is also different. Note that some materials may not be isotropic w.r.t. the elastic modulus as the nature of bond stretching along certain directions will be different. However, let us not go into this right now.
Coming to your primary question, Hardness has a very different dependence on crystal structure. The other answers in this post (Rudiger Rentch and Gert Nolze) have talked about the electronic structure of materials but such relations are more relevant for brittle materials.
For ductile materials the role of crystal structure is the following. It all boils down to the dislocation content and their mobility. If dislocations are mobile and interact with each other, the material will experience higher levels of strain hardening. Similarly, if dislocation interactions lead to recovery, the hardness will be lower. The mobility of dislocations and its energy are important factor. Dislocation energy is related to the dislocation's Burgers vector, which is in turn is related to the lattice parameter of the material. The tendency to form dislocation partials and stacking faults also changes the mobility of dislocations and inter-dislocation interactions, all of which, affect hardness. Cu has a different lattice parameter and SFE (stacking fault energy) than that of Al. Thus the differences in hardness are not surprising.
Another way to understand the idea of dislocation mobility is to look at certain alloying additions. Sometimes, when some trace alloying elements are added to a metal, the modulus does not change much but there is a huge change in the yield strength and hardness. The latter change is solely due to the fact that the addition of some solute reduces the mobility of dislocations, which enhances the hardening effect.
dear Rajorshi, the lattice structure of (pure) materials is only one part in which the internal properties are expressed. The electron configuration of Al (Ne 2s2 p1), where in the most outer electron shell (the 3rd.) there there are 2 on the s-level and only 1 on the p-level. But copper has not only the 3p level filled (6electrons), but also the 4s shell (2 electrons) and has further 10 electrons on the 3d level. It is more than double as heavy than Al. The lattice constant for Cu is only 3.61 angstroem while for Al it is 4.04. This goes along with the higher tensile strength of Cu of about 200 MPa compared to 70 to 160 MPa for Al (depending on purity) as well as higher recrystalization temp for Copper (400-600°C) as Al (290-350). Simillarly the hardness of Al is lower than that of Cu as stress can only be stored in terms of lattice distortion / dislocations until the bonding strength is exceeded.
@ R. Rentsch: I am not very happy about terms like "lattice structure". The term "lattice" is actually referring to a mathematical abstraction of a translation symmetric arrangement of atoms, ions, or molecules and do not have to match at all with atomic positions, see e.g. hexagonal closed-packed materials like Mg, Be, Ti etc., where no atom occupies the corners of the unit cell. I guess, you are talking about the crystal structure. Everything else is perfectly explained :-).
It appears that you are seeking a correlation between hardness and the crystal structure of a material. Unfortunately, such a direct correlation does not exist.
To understand this in detail, it is important to revisit some definitions:
Hardness is the resistance to plastic deformation and is highly dependent on the dislocation mobility of the material.
What you might be more interested in is the Elastic Modulus, which is the measure of the stiffness of a material.
Elastic modulus depends on the absolute value of the bond length and the bond energy (this is the resistance to bond stretching). Although Al and Cu have the same crystal structure, their bond lengths and bond strengths are very different. Hence their modulus is also different. Note that some materials may not be isotropic w.r.t. the elastic modulus as the nature of bond stretching along certain directions will be different. However, let us not go into this right now.
Coming to your primary question, Hardness has a very different dependence on crystal structure. The other answers in this post (Rudiger Rentch and Gert Nolze) have talked about the electronic structure of materials but such relations are more relevant for brittle materials.
For ductile materials the role of crystal structure is the following. It all boils down to the dislocation content and their mobility. If dislocations are mobile and interact with each other, the material will experience higher levels of strain hardening. Similarly, if dislocation interactions lead to recovery, the hardness will be lower. The mobility of dislocations and its energy are important factor. Dislocation energy is related to the dislocation's Burgers vector, which is in turn is related to the lattice parameter of the material. The tendency to form dislocation partials and stacking faults also changes the mobility of dislocations and inter-dislocation interactions, all of which, affect hardness. Cu has a different lattice parameter and SFE (stacking fault energy) than that of Al. Thus the differences in hardness are not surprising.
Another way to understand the idea of dislocation mobility is to look at certain alloying additions. Sometimes, when some trace alloying elements are added to a metal, the modulus does not change much but there is a huge change in the yield strength and hardness. The latter change is solely due to the fact that the addition of some solute reduces the mobility of dislocations, which enhances the hardening effect.
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