Determination of dynamic and static displacements of atoms in crystal lattice of the titanium carbide by weakening of neutron diffraction maxima

The Fifth Conference “ Nuclear Science and Its Application”, 14-17 October 2008

DETERM INATION OF DYNAM IC AND STATIC DISPLAC EM EN TS O F

ATOMS IN CRYSTAL LATTICE OF THE TITANIUM CARBIDE BY W EA K ­

ENING OF NEUTRON DIFFRA CTIO N M AXIM A

I. KHIDIROV. * KH. SH. KHOLMEDOV

Institute o f Nuclear Physics, Uzbekistan Academy o f Sciences, Tashkent, Uzbekistan *Tashkent University o f Information Technologies, Tashkent, Uzbekistan

The atomic mean-square displacement W in interstitial solid solutions or interstitial phases is combined of amplitude thermal vibrations and static displacement of atoms:

Uİ

Uln

I 2

where y 2, is dynamic displacement caused by thermal vibrations, Ustat is static display-cement caused oy both difference o f atom sizes and deviation of solid solution composition from stoichiometry. Both factors cause decreasing o f diffraction maxima under the identical law:

I = I0exp-

3X2 (« 2 + u 2dyn ~ **stat),

were I0 is intensity of diffraction maximum in the absence of displacements, 0 is the angle

of Bragg, X is wavelength of neutrons, y f depends whereas Ustat does not depend on temperature. It allows one to determine separately these parameters in introduced cubic structure phases by measuring neutron diffraction pattern at room temperature and temperature of liquid nitrogen. In the given work the amplitude o f thermal fluctuations and static displacements of atoms in titanium carbide for the first time are separately determined in homogeneity ranges by neutron diffraction.

The Fifth Conference “ Nuclear Science and Its Application”, 14-17 October 2008

It is established that static distortion in the stoichiometric carbide is negligibly small. It

is revealed that amplitude o f thermal vibrations of atoms -y both at room temperature, and at

temperature of liquid nitrogen and static distortions \ u stat in titanium carbide linearly increase with reduction of concentration of carbon with the greater rate up to concentration C/Ti = 0.88 than at lower concentration of the carbon. Based on the established concentration dependence of amplitude of thermal vibrations of atoms it is possible to draw a conclusion that forces of interaction between atoms in titanium carbide decrease with the big rate in the initial stage of concentration deviation of the carbon from stoichiometric, and further - this process is slowed down.

It is established, that between experimentally determined values of total root-mean- square displacement of atoms and amplitudes of thermal fluctuations at two temperatures equality

(Tl=300 K) - Udyn (T2=78 K) is well observed.

U

(T1=300K) - U (T2=78K) = u ,