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Tuesday, January 26, 2016


An “event” is anything that happens at some definite locations at some definite time. Typical examples are your birth, assassination of Abraham Lincoln etc. In contrast, a forest fire that sweeps across 10000 acres in 5 days does not constitute an “event” because the fire is spread out in space and time.
The adjective “definite” means   “distinct” or  “limited” for any one observing the happening.

  • Spatially separated events that are simultaneous in one frame are, in general, not simultaneous when viewed from other reference frame.
  • Simultaneity is a relative concept, but not an absolute one.
  • The concept of simultaneity between two events in different space points has an exact meaning only in relation to a given inertial system i.e. “Each frame of reference has its own particular time”.
  • To measure the length of an object means to locate its end points simultaneously. As simultaneity depends on frame of reference, the length measurements will also depend on frame of reference.
  • Thus, “The length i.e. Space is a relative concept, not an absolute one”.
  • Thus there is no such thing as an absolute, global “now”.

Sunday, January 17, 2016

Whar are Miller Indices?

The concept of Miller Indices is to describe the various directions and positions of atoms in crystals. Any point within the given Lattice can be considered as origin. The crystallographic axis a,b&c can be considered as the 3 coordinate axes. So these 3 axes can be selected along 3 crystallographic axes.

Consider the plane to be indexed. Note down the intercept made by the plane on the three crystallographic axes, intercepted by translation vectors.

Let the intercepts be 3a, 2b, 4c, i.e. 3, 2, 4. Find out the Reciprocal of intercepts 1/3, 1/2 & 1/4.

Convert them in to a set of integers: 4, 6 & 3.

This set of integers are represented in Parenthesis -- (4,6,3)

The set of three integers is known as Miller Indices of Plane.

In general, the Miller Indices are represented by (h,k,l)

The set of 3 numbers (h,k,l) so obtained are known as Miller Indices and conventionally enclosed in parenthesis.

These set of numbers defines the planes and also the family of Planes Parallel to it and equally spaced.

It is clear that Planes 1,2 & 3 have intercepts only on the crystallographic axis a. They all are separated by equal distances.

The intercept of Plane1 on axis a is at distance ‛a’. Therefore the intercept is (a, ∞,∞).

Take the intercepts as (1, ∞,∞).

Reciprocate them : 1/1, 1/∞, 1/∞ ---- (1,0,0)

Therefore the Miller indices of Plane 1 are (1,0,0).

In case of Plane 2 intercepts are (2, ∞,∞)

Now (h,k,l) = 1/2, 1/∞, 1/∞ = (1,0,0)

In case of Plane 3 intercepts are (3, ∞, ∞)

Hence, (h,k,l) = (1,0,0)

By taking the Reciprocal of all Planes inside a single unit cell, we can discuss all crystal Planes in terms of Planes passing thru a single Unit cell.

The fractions are converted in to smallest set of integers for convenience. If (h,k,l) are miller indices the Plane intercepts the Unit cell at a/h, b/k, c/l

In the above figure, the intercepts are given by (3, 2, 1)

Reciprocal of intercepts = 1/3, 1/2, 1/1 = (2,3,1)

Therefore, (h,k,l) = (2,3,1)

If an intercept is at infinity, the plane is parallel to one of coordinate axes, the corresponding index is zero.

If a Plane cuts an axis on negative side of origin the corresponding index is negative and is indicated by placing a minus sign above the index.


The indices of a direction, are simply the vector components of the directions resolved along each of the coordinate axis and reduced to small integers.

In a cubic Unit Cell, if the origin is at the corner and the axes are parallel to the edges, body diagonal would be represented as [111].

A Lattice point n1a+n2b+n3c lies in the direction [n1 n2 n3].

n1, n2 & n3are integers.

The use of square brackets around the numbers [111] denotes that they refer to a crystallographic direction.

In the same way ‛+a’ axis have indices [1,0,0] and similarly ‛-a’ axis have indices [1,0,0] and for ‛+b’ axis [0,1,0] and ‛-b’ axis [0,1,0].

In general the direction of a line perpendicular to a plane having miller indices (h,k,l) is given by [h k l]


Positions or points are specified as in any other coordinate system namely by 3 numbers each of which refers to distance along the axis expressed as multiples of Lattice constant.

The coordinates of the center point of cubic unit cell are [1/2,1/2,1/2]

The coordinates of the face centers are [1, 1/2, 1/2]

Friday, January 15, 2016

Difference between Temperature and Heat

Heat is a form of (Thermal) energy due to the kinetic energy of molecules in a substance. Temperature is measure of hotness or coldness of a body. Temperature is a measurement of the average kinetic energy of the molecules in an object or system.

Mathematically, dQ = k dT; where dQ is the change in heat content, k is a constant of proportionality, and dT is the change in temperature (usually in degrees Kelvin).


Absolute Zero could be defined in different ways as follows:

Absolute Zero is a state of minimum molecular movement

Absolute zero is that temperature at which disorder of a system reaches its minimum value.

Absolute Zero is a state of zero Entropy.

Absolute Zero is the temperature at which a “Heat Engine” can operate at 100 percent efficiency.

Absolute zero is the point where no more heat can be removed from a system, according to the absolute or thermodynamic temperature scale. This corresponds to 0 K or -273.15°C. In classical kinetic theory, there should be no movement of individual molecules at absolute zero.

A system at absolute zero will not have enough energy for transfer to other systems. It is therefore correct to say that molecular kinetic energy is minimal at absolute zero i.e; the motion of molecules in a system is least at absolute zero

Absolute zero is defined as 0 (zero) K on the Kelvin scale and as −273.15°C on the Celsius scale. This equates to −459.67°F on the Fahrenheit scale.

The third law of thermodynamics says absolute zero is not obtainable in a finite number of steps (and it is impossible to practically have an infinite number of steps.

You couldn't send a current through a wire at absolute zero because the electrons would not move.
The critical point when there is more resistance is absolute zero itself.

The ideal gas law says that PV=nRT. This means that in order for the temperature to be 0 (absolute 0), P or V would have to be zero. An actual gas cannot have a Pressure or Volume of zero and still have mass. This is a reason while absolute zero is unobtainable.

What is triple point of water?

The triple point of any substance is that temperature and pressure at which the material can coexist in all three phases (solid, liquid and gas) in equilibrium.Triple point of water is a single point in P-T phase diagram of water where the three phases of water coexist.

The triple point of water is defined to take place at 273.16 K, where K is the SI unit Kelvin. Unlike Celsius and Fahrenheit scales, Kelvin is not measured using degrees; we merely say "Kelvin."
It is important to note that the pressure the triple point exists at is 4.58 torr in SI units or .006 atm.