**10. References**

418 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

4. The thermodynamic analysis, performed by taking into account the formation of solid lower-valent fluorides and excess enthalpy of atom interaction during crystallization, showed that the moving force of CVD of the alloys from the W-M-F-H systems (the

5. A lot of applications of tungsten coatings, deposited from tungsten hexafluoride and hydrogen mixture at low temperature, as well as tungsten alloys and carbides are

This work was supported by the Russian Foundation for Basic Research, project No. 09-08-

tungsten yield rise under its alloying with rhenium and molibdenium.

supersaturation in these systems) increase in order: Ta, Nb, V, Mo, W, Re.

reviewed in this chapter.

Description of symbols used in the text

Ω Atomization energy

n Valency of metal Δf Н Formation enthalpy

Zm Atomic number of metal Zx Atomic number of halid

Δs Н Sublimation enthalpy

Δf Но298 (g) Standart formation enthalpy at 298 K at gaseous state Δf Но (s) Standart formation enthalpy at 298 K at solid state

Δs Hо298 Standart sublimation enthalpy at 298 K Sо298 (g) Standart entropy at 298 K at gaseous state Sо298 (s) Standart entropy at 298 K at solid state

Ср Specific heat at constant stress Δ Нm Partial enthalpy of mixing

m Standart mixing enthalpy

ΔsH Partial molar enthalpy

Symbol Description

М Metal Х Halid

at Atom φ Function

ψ Functional

S Entropy

∆H0

**8. Acknowledgments** 

**9. Appendix 1** 

182.

components and the atom intraction on the growing surface during the crystallization. It was established that only an introduction in the thermodynamic calculation of atom interaction on the growing surface, which increase in the following sequence: Ta, W, Re, Nb, V, Mo, results in a rise of yield of VB group metals under their co-deposition with tungsten, excepting W-Ta system. This may explain the experimentally observed


**16** 

Toufik Zebbiche

 *Algeria* 

*University SAAD Dahleb of Blida,* 

**Effect of Stagnation Temperature on** 

The obtained results of a supersonic perfect gas flow presented in (Anderson, 1982, 1988 & Ryhming, 1984), are valid under some assumptions. One of the assumptions is that the gas is regarded as a calorically perfect, i. e., the specific heats *CP* is constant and does not depend on the temperature, which is not valid in the real case when the temperature increases (Zebbiche & Youbi, 2005b, 2006, Zebbiche, 2010a, 2010b). The aim of this research is to develop a mathematical model of the gas flow by adding the variation effect of *CP* and γ with the temperature. In this case, the gas is named by calorically imperfect gas or *gas at high temperature*. There are tables for air (Peterson & Hill, 1965) for example) that contain the values of *CP* and *γ* versus the temperature in interval 55 K to 3550 K*.* We carried out a polynomial interpolation of these values in order to find an analytical form for the function

The presented mathematical relations are valid in the general case independently of the interpolation form and the substance, but the results are illustrated by a polynomial interpolation of the 9th degree. The obtained mathematical relations are in the form of nonlinear algebraic equations, and so analytical integration was impossible. Thus, our interest is directed towards to the determination of numerical solutions. The dichotomy method for the solution of the nonlinear algebraic equations is used; the Simpson's algorithm (Démidovitch & Maron, 1987 & Zebbiche & Youbi, 2006, Zebbiche, 2010a, 2010b) for numerical integration of the found functions is applied. The integrated functions have high gradients of the interval extremity, where the Simpson's algorithm requires a very high discretization to have a suitable precision. The solution of this problem is made by introduction of a condensation procedure in order to refine the points at the place where there is high gradient. The Robert's condensation formula presented in (Fletcher, 1988) was chosen. The application for the air in the supersonic field is limited by the threshold of the molecules dissociation. The comparison is made with the calorically

The problem encounters in the aeronautical experiments where the use of the nozzle designed on the basis of the perfect gas assumption, degrades the performances. If during the experiment measurements are carried out it will be found that measured parameters are differed from the calculated, especially for the high stagnation temperature. Several reasons

**1. Introduction** 

*CP(T).*

perfect gas model.

**Supersonic Flow Parameters with** 

 **Application for Air in Nozzles** 

