# br Conclusions After the study of the

Conclusions
After the study of the relation between film stress and deposition process parameters of Si3N4 film, and the relation between etching selectivity and etching parameters, the following conclusions have been reached.

Acknowledgements
Sponsored by Project for Optoelectronic Applications (40405030104) and Basic Research Project OF National Defense (A0920110019).

Introduction
Force constant of a propellant, fv, also known as propellant force or propellant impetus, is one of the Concanamycin A cost features of a propellant, and also an important ballistic character of the propellant. It could be expressed aswhere is gas constant for a unit mass of burned propellant gas； Tv is adiabatic flame temperature of a propellant at constant volume

Comments
The first statement: propellant force is “the work done by the gas products of a kilogram of burned propellant during the expansion process from 0 K to Tv K at 1 atmospheric pressure” [1,2].
The second statement: propellant force is “the work done by the gas products at temperature of Tv K after the burning of a kilogram of propellant during the free expansion process at atmospheric pressure” [3,4].
The third statement: propellant force is “the energy released by the decomposition of a unit mass (a kilogram) of propellant” [5,6] or “the maximum amount of work which can be done by unit mass of propellant” [6,7].
According to the first statement, the expansion work A done by the gas products could be calculated bywhere Pext is exterior pressure/surrounding pressure； V is gas/system volume； p is gas/system pressure; pa is atmospheric pressure.
The reason for the use of generalized integration during the above calculation is that the above relationship could only be established at constant pressure (p = pext = pa). In this case, the pressure term could be moved from after the integral sign to before the sign. And also only in this case, the product pV could be applied to the ideal gas state equation. As the initial state of the process under consideration is at 0 K, the thermal movement of the gas molecules should be absolutely stopped. The collision of the molecules against the walls of the container would thus never occur， and the gas pressure should be zero. In other words, the initial state could not provide the condition of the constant pressure process. Furthermore， the ideal gas state equation would be meaningless at that state point. To avoid this, a state at a temperature slightly higher than 0 K can be taken as the initial state, thus the gas in the system would have the pressure p = pa and a minute volume of δV. Let δT or δV approach infinitely to zero, the result value of the work could be obtained.
The work A in the first definition could also be calculated in another way. One could calculate the increment of the gas volume during the process of a temperature increase of dT at temperature T and volume V under constant pressure. For the ideal gas expansion process under constant pressure, the expansion coefficient at constant pressure would bewhere α is the expansion coefficient of burned propellant gas at constant pressure; T is the gas/system temperature.
Thus,and the work done in this minute process should be
The work done during the whole process could be expressed as
Though the value of the propellant force in this definition is equal to the value of the work done during the physical process numerically, the definition itself could not reflect the essence of the propellant force. It is obvious that as a kind of energy source, the work done by the propellant combustion gas should conduct spontaneously at the expense of the energy decrease of the gas (from higher temperature and pressure to lower ones). The first definition, describing propellant force as the work done during the gas expansion process by outside heating, is really of no physical meaning.
In thermodynamics, “free expansion” and “expansion against outside pressure” are very different concepts. The former refers the system experiencing an expansion process against vacuum surroundings, i.e., the outside pressure is zero. The work done would be