Evolution of distance between ω particles in metastable β-Ti alloy determined from in-situ small angle neutron scattering

The evolution of distance between ω particles in metastable β Ti15Mo alloy (8.1 in at. %) was determined from in-situ small angle neutron scattering (SANS). SANS data were recorded during heating of the material from room temperature to 600 ◦C with the heating rate of 1 ◦C/min. The results agree with previously determined ordering of ω particles in a cubic three-dimensional array with the axes along the cubic axes 〈100〉β of the host lattice. The distance between particles, which increases with temperature, was investigated in three orientations with the incident beam parallel to [100]β, [110]β and [111]β.

ω iso phase is stabilized by an irreversible diffusion-controlled rejection of β stabilizing elements from ω iso particles. ω iso particles typically coarsen during annealing and are weakly ordered in a cubic array along 100 β directions [8].

Material
In this research a single crystals of metastable β-titanium alloy Ti-15Mo (8.1 at. % of Mo) were studied. This alloy is used mainly for biomedical applications. It was originally developed for the chemical industry to provide a titanium alloy with improved corrosion resistance, low elastic modulus, high strength, good fatigue resistance, and good ductility. High temperature applications were also investigated but thermal handling difficulties and microstructure instability at moderate temperatures prevented the extended use in the aerospace industry [9].

Preparation of single crystals
The diffraction experiments were performed on single-crystalline Ti-15Mo. The single crystals were grown in the optical furnace from a rod with diameter of 9 mm. The furnace was evacuated by a turbomolecular pump up to 10 −6 mbar to avoid oxidation of the titanium alloy. After proper evacuation the quartz chamber was filled with high purity Ar protective atmosphere. At the beginning of each crystal growth, a neck was created in order to isolate one grain. The pulling rate was 10 mm/h and the rotation velocity of both the upper and the lower shaft was 5 rpm. The total length of grown crystals was up to 9 cm. A thorough explanation of the growth process can be found in [10].

Electrical resistance
Measurements of electrical resistance of the samples were performed employing a self-made apparatus. A four-point methods of electrical resistance measurement was employed. The scheme of electrical circuit of this technique is shown in Fig. 1a. Due to the setup of this method, the resistance of contact leads and their welds with the sample does not affect the measured electrical resistance. The current is the same at all points in the circuit. As only voltage drop across the sample is measured (and not the wires resistances), the calculated electrical resistance represents solely the resistance of the sample (R sample ). The numbers 1 -4 in Fig. 1a label wires, which were welded to respective contacts on the sample (see Fig. 1b).
The voltage was measured simultaneously with the electrical current utilizing nanovoltmeter Keithley 2182 and SourceMeter Keithley 2400 device, respectively, which allows relative measuring error to be less than 10 −4 at each measured point while acquiring about 2 points per second [11]. There are two heating elements placed on top and underneath the sample, respectively. Each heating coil has its own source (Kikusui PAS-40-18), which provide current used for heating. The temperature is measured by K type thermocouple placed in a vicinity of the sample. Measured samples were flat of the thickness slightly less than 1 mm and the size of 15 × 10 mm 2 . They were cut to the shape of letter S to increase the effective length of the sample for electric current flow and four contacts were appropriately joined. The samples shape and dimensions are shown in Fig. 1b

Small angle neutron scattering
Small angle neutron scattering (SANS) experiments were measured at three orientations of the single crystal sample (111) β , (110) β and (100) β of β phase with corresponding plane perpendicular to incident neutron beam direction. Samples were installed in vacuum high temperature furnace and one by one heated with the heating rate of 1 • C/min from room temperature up to 600 celsius. SANS experiments were performed at the Helmholtz-Zentrum Berlin (HZB), Germany, at the instrument V4 [12,13]. Neutrons were recorded on a twodimensional (2D) gas detector of 128 × 128 pixels of 5 × 5 mm 2 in so-called list-mode and afterwards binned by time frames of 5 minutes, which corresponds to temperature range of 5 celsius. The sample-to-detector distance was set to 15.8 m, collimation to 12 m and the wavelength was kept at (5 ± 0.5) Å. The measured data were calibrated using water and corrected by standard measurements of cadmium background. Scattering of the sample in high temperature furnace was used as "buffer" background. Sketch of the V4 instrument can be found in [14].

Electrical resistance measurements
It was shown that phase transitions in Ti alloys can be detected by means of electrical resistance measurement that is particularly sensitive to evolution of ω phase particles [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Fig. 2 shows the evolution of normalized electrical resistance (R/R 20 ) of Ti-15Mo alloy during heating with the heating rate of 1 • C/min, where R 20 is the electrical resistance of the sample either at 20 • C. The evolution of resistance in metastable β Ti-15Mo alloy exhibits two significant drops due to ongoing phase transformations. The first decrease of the electrical resistance between room temperature and 200 • C is attributed to dissolution of ω ath [19,21,23,29]. Further heating results in increase of the electrical resistance, which is caused by increasing electronphonon scattering coupled with formation of ω iso [29]. The second decline of the electrical resistance (between 335 • C and 560 • C) by further coarsening of ω particles coupled with decrease of volume fraction of ω phase [30]. During heating above 560 • C, the resistance increases and the concentration of α phase first increases to reach an equilibrium and than close to β-transus decreases again. Above the β-transus (about 730 • C -note a small change of slope of the curve in Fig. 2 at this temperature) α phase dissolves completely.

SANS
In this study we investigated Ti-15Mo single crystals in three orientations of primary beam with respect to β matrix. The SANS diffraction patterns of these samples with the incident beam perpendicular to (100) β , (110) β and (111) β is shown in Fig. 3. The results confirm the spatial ordering of ω particles in a cubic three-dimensional array with the axes along the cubic axes 100 β of the β matrix determined from small angle X-ray scattering [8].  The evolution of the lattice parameter of a cubic three-dimensional array of ω particles, which was determined from the SANS diffraction patterns measured in-situ during heating with heating rate of 1 • C/min is shown in Fig. 4. The values are presented only in the temperature interval of 445 • C -550 • C. Bellow this temperature, ω particles were too close to each other and the peaks corresponding to these distances were outside of the detector. With the increasing temperature the diffraction maxima approached center of the detector and at temperatures above 550 • C hid behind the beamstop and subsequently disappeared due to dissolution of ω phase at 560 • C [28,30].
The lattice parameters were determined by fitting position of peaks in regions highlighted by white line in Fig. 3 (along 100 β ) for the [100] β and [110] β orientations of the primary beam (for [100] β quasi-peaks were fitted, since no clear peaks can be observed in this orientation). Due to low intensity of the peaks in the [111] β orientation of the primary beam, lattice parameters were not determined in this case.
The decrease of electrical resistance in the temperature interval of 445 • C -550 • C is accompanied by coarsening of ω particles, which have size about 15 nm at 420 • C (see Fig. 5) and about 50 nm at 550 • C [28]. The coarsening is accompanied by an increase of the distance between ω particles. The lattice parameter of the cubic three-dimensional array of ω particles is approximately equal to their size. The lattice parameter determined from

Summary
We have studied evolution of positions of ω particles with respect to each other in single crystals of metastable β titanium alloy Ti-15Mo by SANS. We determined the particles distance during heating and confirmed that the particles order in a cubic three-dimensional array with the axes along the cubic axes 100 β of β matrix.