THERMODYNAMIC, THERMAL AND ELASTIC PROPERTIES OF TITANIUM NITRIDE TiN: COMPARISON OF VARIOUS DATA AND DETERMINATION OF THE MOST RELIABLE VALUES

Abstract

The analysis of literary data on thermodynamic, thermal and elastic properties of titanium nitride TiN which included values Debye temperature θD, volume coefficient of thermal expansion αV and bulk modulus B under standard conditions is carried out. It has been shown that the known data have a significant spread of values from 20 to 43 %. The 8 most rational variants of optimizing calculations are proposed, which make it possible to reveal the most reliable values of some TiN parameters. At the same time, the minimum and maximum values of θD and αV were used from literary sources, as well as the least contradictory data on isobaric heat capacity Cp, melting temperature Tm.p and density d of TiN. To improve the calculated results, the values of θD(TiN) determined using the methods of Magnus ‒ Lindeman and Debye were also used. The Mayer’s relation was the basic test expression. The obtained values of the bulk modulus were compared with the literature data. This made it possible to distinguish the least and most reliable values of αV and θD, as well as make a refinement correction for the last value. As a result, it was found that under standard conditions, the value of θD(TiN) close to the optimal should be within 746‒769 K, and for its isochoric heat capacity CV ‒ in the range 36.55‒37.19 J/(mol×K). The range of values, after optimization, does not exceed 3 %, unlike the 20 % available in the literature. A more accurate definition of Debye temperature for TiN needs to radically refine the values of its αV and B

Ion-beam assisted sputtering of titanium nitride thin films

“…This model’s expression for the behavior of can be shown as 36 where is the superconducting critical temperature of a bulk sample, b is the characteristic length of electron wave leakage, and N (0) V is the BCS coupling constant. By using known values for the Debye temperature (for TiN of 746–769 K 38 ), and the superconducting energy gap of 3 meV, we can extract the BCS coupling of N(0)V = 0.165 and use it to determine the leakage parameters in our films. Considering the disordered nature of sputtered films, one can further modify Eq.…”

Unfolding the Origin of the Ultrafast Optical Response of Titanium Nitride

“…where 𝛽 = −3Y𝛼 L /𝜌 is a constant, containing the Young modulus Y = 300 GPa (highest value in the temperature range considered in [64]), the linear expansion coefficient 𝛼 L = 8.3 × 10 −6 K −1 and the density 𝜌 = 5.21 × 10 3 kg m −3 of TiN. [65,66] By solving the above equation, the deformation 𝜂(z, t) along the z-direction is retrieved at each temporal delay (see Section 7 for details), and then the skin layer thickness variation can be determined as Δd 0 (t) = ∫ d 0 0 𝜂(z, t)dz. This modulation is in turn responsible for a plasma frequency modulation in the skin layer, which can be computed as:…”

“…The phenomenon can be properly described by the D'Alembert equation for the displacement u along z ‐direction, with the temperature as driving term: $$$$\begin{equation} \frac{\partial ^2 u(z,t)}{\partial t^2} = v^2\frac{\partial ^2 u(z,t)}{\partial z^2} + \beta \frac{\partial T(z)}{\partial z} \end{equation}$$$$where β = −3 Y α L /ρ is a constant, containing the Young modulus Y = 300 GPa (highest value in the temperature range considered in [64]), the linear expansion coefficient α L = 8.3 × 10 −6 K −1 and the density ρ = 5.21 × 10 3 kg m −3 of TiN. [ 65,66 ] By solving the above equation, the deformation η( z , t ) along the z ‐direction is retrieved at each temporal delay (see Section 7 for details), and then the skin layer thickness variation can be determined as $$\Delta d_{0}(t) = \int _0^{d_{0}}\eta (z,t) \mathrm{d}z$$. This modulation is in turn responsible for a plasma frequency modulation in the skin layer, which can be computed as: $$$$\begin{equation} \Delta \omega _P(t) = -\frac{1}{2}\frac{\omega _P}{d_{0}}\Delta d_{0}(t).$$…”

Ion-beam Assisted Sputtering of Titanium Nitride Thin Films

“…where T c ∞ is the superconducting critical temperature of a bulk sample, b is the characteristic length of electron wave leakage, and N(0)V is the BCS coupling constant. By using known values for the Debye temperature θ D (for TiN of 746-769 K 36 ), and the superconducting energy gap ∆ of 3 meV, we can extract the BCS coupling of N(0)V = 0.165 and use it to determine the leakage parameters in our films. Considering the disordered nature of sputtered films, one can further modify Eq.…”