Paris-Edinburgh Cell Workshop 2013

May 23-24, 2013, Advanced Photon Source, Argonne National Laboratory

Hands-on Trainings

Table of Contents

Course 1: PE cell assembly preparation - Tony YuCourse 2: PE cell high-pressure experiment - Curtis Kenney-BensonCourse 3: Ultrasonic measurement in PE cell - Yoshio KonoCourse 4: Liquid/amorphous EDXD Data Analysis and Falling Sphere

Viscometry Demonstration -Changyong Park

Training Course 1: PE cell assembly preparation

Tony Yu

This training course provides an opportunity to practice using PE cell parts for use in a high-pressure experiment. Trainees will get a feel for the ceramic parts and assemble them for an actual experiment in the high-pressure PE press (Training Course 2).

Training procedures1. Understand a standard PE cell design and parts.2. Assemble PE cell parts for high-pressure experiment in training course 2.

A standard PE cell assembly design in HPCATA standard PE cell assembly has been designed for stable high-pressure and high-temperature

experiments up to around 7 GPa and 2000 °C. Cup-shaped WC anvils with the cup diameter of 12 mm and the bottom diameter of 3 mm are used to generate high pressures (e.g. Yamada et al., 2011). The cell assembly mainly consists of a boron-epoxy (BE) gasket, an MgO ring, ZrO2 caps, a graphite heater and a BN sample capsule. Large volume samples of up to 2 mm in both diameter and length are accommodated by this cell assembly. A ring-shaped BE is used as gasket with a supporting outer Lexan ring. The BE gasket and ZrO2 caps in the assembly provide good thermal insulation for high temperature experiments. An MgO ring is placed between BE gasket and graphite heater to increase stability of the cell assembly and maintain anvil gap. High temperature is generated by the graphite heater. The sample for this training is a mixture of GeO2 and B2O3 powder, and trainees will melt the sample in training course 2.

Procedures to assemble standard PE cell

(1) Assemble Lexan ring, Boron-epoxy gasket, and MgO ring.

(2) Put graphite heater in the Assembly (1), and attach ZrO2 middle cap at the both ends of graphite heater.

(3) Put glue on ZrO2 cap (Do not glue on graphite heater) and attach molybdenum foil over the graphite heater. Put ZrO2 top cap on it and glue at the slope of the ZrO 2 caps. Then, put silver-paste glue on the side of tantalum rod and insert the tantalum rod into the top ZrO2 cap.

(4) Flip the assembly (3). Pack sample powder in BN capsule. Put BN capsule with sample powder in the assembly (3), and close with BN cap.

(5) Similarly to process (3), attach molybdenum foil, ZrO2 top cap and tantalum rod.

ReferenceYamada, A., Y. Wang, T. Inoue, W. Yang, C. Park, T. Yu and G. Shen, Review of Scientific Instruments 82,

015103-015107 (2011).

Training Course 2: PE cell high-pressure experiment

Curtis Kenney-Benson

This training course provides an opportunity to conduct a high-pressure and high-temperature experiment using a VX5 type Paris-Edinburgh (PE) press. Trainees will operate the hydraulic pump system to increase pressure and resistive heating to melt the GeO2-B2O3 sample.

Training procedures1. Understand PE press components.2. Setup a PE cell in the press.3. Increase pressure.4. Heating.5. Quench the molten sample and decompress. 6. Check the sample by opening cell assembly.

High-pressure and high-temperature experiment using standard PE cellThe standard PE cell is capable of high-pressure and high-temperature experiment up to around

7 GPa and 2000 °C. Figure 1 shows an example of pressure generation curve and temperature calibration curves. The standard cell assembly uses 12 mm cup anvils to generate pressures to around 7 GPa at room temperature. The use of smaller anvil sizes increases pressure efficiency, and we are developing cell/anvil combinations to generate higher pressures. Temperature calibration has been carried out up to 2000 °C and up to 97 tons, which corresponds to ~6 GPa. We fit these data to a two dimensional (power and load) polynomial equation and use these temperature calibration curves to estimate temperature in liquid structure measurement.

ReferenceKono, Y., C. Park, C. Kenney-Benson, G. Shen, and Y. Wang, Physics of the Earth and Planetary Interiors,

under review.

Figure 1 (Kono et al., under review)

Training procedures

Paris Edinburg Press Components

The PE press used at HPCAT has two primary systems for sample environment control: a pressure building system and a high temperature heating system. Cell pressure is increased by a two stage hydraulic system located at the bottom of the portable PEC control rack. The schematic for the hydraulic system is shown in Figure 2. The initial compression (up to ~3000 psi) is accomplished through the use of the low pressure pump. In order to reach higher pressures (up to 20,000 psi) the high pressure portion of the system is isolated by closing valve 1, and pressure is increased by engaging the High Pressure Generator. The sample heater power supply is located just above the hydraulic system in the PEC control rack. The sample temperature can be controlled by changing the power delivered to the cell as illustrated in Fig. 1. The PC at the top of the rack is used to control the power delivered to the cell, as well as monitoring the pressure in the hydraulic system.

Loading a cell in the press

The assembled PE Cell from training #1 should be placed onto the lower anvil before manually lowering the upper anvil down to touch the top of the cell. Stop as soon as contact with the cell is made. During this process, care should be taken that the tantalum wire electrodes do not fall from the cell, and that the orientation of the cell is upright. Carefully place the shield over the press, aligning the notch on the shield to avoid hitting the lower anvil electrode/cooling block.

Increase pressure

To compress the PE cell follow these steps. Safety goggles must be worn throughout the procedure.

Open valves 1, 2 and 3, and close the vent cap on the low pressure pump.

Close the check valve on the low pressure pump.

Use the low pressure pump to increase oil pressure, to about 400 PSI.

Make all water and electrical connections on the press (see Heating below).

Use the low pressure pump to increase oil pressure, to about 3000 PSI.

Close the low pressure pump isolation valve (Valve 1).

Turn the handle on the high pressure generator clockwise to increase pressure to 5,000 PSI.

Heating

The heater current follows a path from the lower anvil, through the tantalum wires, to the heater and then out the upper anvil/press body. The lower anvil is electrically isolated from the rest of the press by a Kapton sheet below the anvil, and a PEEK plastic ring around the anvil. When current is applied to the heater, these plastic parts are at risk, so cooling blocks are attached to each anvil to carry away excess heat. Once the sample is compressed to 400 psi, follow these steps:

Attach the cooling water lines to each anvil. Turn the cooling water valves on. Set the position of the manual output switch mounted just below the Hewlett- Packard power

supply in the rack to “OUTPUT DISABLED”. It is now safe to handle the high current cables. Attach the cable with the red band to the lower anvil cooling block. Attach the cable with the black band to the top of the press body. Complete the compression to the target pressure. Set the output switch to “OUTPUT ENABLED”. Open the user interface on the control computer if not already running. Push the red “Clear Faults” button at the lower right of the user interface. Set the incremental adjustment on the power level to 1 watt. Set the target power to zero. Turn the Power Output on. Set current limit to 200. Turn the PID control on. Slowly increase the power level to raise the temperature (~1 W/sec.). When the power level reaches 340 watts, let the power remain constant for 5 min.

Quench the molten sample and decompress

After the 5 minute heating period, quench the sample by turning the PID control off, then push the “Output Off” button on the user interface and set both the target power and voltage to zero. Switch the manual output switch to “OUTPUT DISABLED” and wait until the temperature of the press surface is lowered enough to touch safely. Remove the heater cables from the press. Allow the cooling water to run for 5-10 min. to assure that the anvils have cooled. Turn off the cooling water flow and disconnect the water lines. Decompress by rotating the high pressure generator counterclockwise until the pressure is approximately 3000psi. Slowly open Valve 1 to equalize pressure between the two stages of the hydraulic system. Open the vent cap on top of the low pressure pump, then slowly open the check valve. Once the pressure reads zero, manually retract the upper anvil and remove the cell from the press with a pair of tweezers.

Check the sample by opening cell assembly

Return to the sample lab and cut the cell open. The cells have a tendency to shatter when cut, so be careful to contain the cell fragments. Find the central graphite/BN core and shave it open with a razor blade to reveal the sample material.

Training Course 3:

Ultrasonic measurement in PE cell Yoshio Kono

This training course provides an opportunity to use ultrasonic measurement in the PE cell for measuring elastic wave velocities at high pressure and high temperature conditions. Trainees will operate ultrasonic measurement equipment to collect ultrasonic signal data and will conduct data processing to determine elastic wave travel time by using a locally developed macro program on Igor Pro.

Training procedures1. Understand ultrasonic measurement setup.2. Operate ultrasonic measurement equipment and collect ultrasonic signal data.3. Analyze elastic wave travel time using a locally developed macro program on Igor Pro.

Experimental setup

We will conduct an ultrasonic measurement of SiO2

glass simplified from the study of Kono et al. (2012). In order to generate and receive ultrasonic signals in PE cell, a 10°Y-cut LiNbO3 transducer is attached to the back side of the top WC anvil. The 10°Y-cut LiNbO3 transducer has the capability to generate and receive both compressional and shear waves simultaneously. The transducer is connected to a co-axial cable, which goes through a hole at the top of the PE press. This co-axial cable connects to the ultrasonic equipment (pulse generator, oscilloscope, and amplifier), which are located outside the 16-BM-B hutch. A pulse generator (Tektronix AFG3251) generates 20 MHz (for shear wave) and 30 MHz (for compressional wave) electrical sine waves, and the electrical signal is divided into two directions by a directional bridge (Agilent RF Bridge 86205A) (Fig. 1). One signal is directed to the oscilloscope through a -40 dB attenuation path and the other signal goes to the LiNbO3 transducer through the directional bridge.

Elastic waves generated by the LiNbO3 transducer pass through the WC anvil and propagate into the Al2O3 buffer rod and the SiO2 glass sample (Fig. 2). A series of reflected elastic wave signals came from the interfaces of anvil/buffer rod (R0), buffer rod/sample (R1), and sample/backing reflector (R2). This series of reflected signals and the attenuated input signal are amplified by a 40 dB amplifier with a bandwidth of 0.2-40 MHz (Olympus Model 5678 Ultrasonic Preamplifier) (Fig. 1).

Figure 3a shows an example of waveform obtained for the SiO2 glass sample. The data show clear reflected signals of R0, R1, and R2 for both compressional and shear wave. The elastic wave travel time was determined by the pulse echo overlap method using the reflected signals from the buffer rod/sample (R1) and sample/backing reflector (R2) interfaces (Fig. 3b).

Data acquisition

Figure 2

Figure 1

Figure 2

The pulse generator can be controlled by the ArbExpress software installed on the oscilloscope PC. In ArbExpress, you only need to change the parameter ‘Output Frequency’. The ‘Output Frequency’ in ArbExpress is frequency for 3-cycle sine wave, the input of ‘Output Frequency’ is the value of the target wave frequency divided by 3.

1. Input 6.67M (for 20 MHz shear wave) or 10M (for 30 MHz compressional wave) in ‘Output Frequency’ window in ArbExpress, and then press ‘Apply’ button. Please confirm capital M (indicates Mega Hz). 2. Go to oscilloscope application ‘TekScope’.3. Press ‘Run/Stop’ button, and refresh ‘CH1’ by turning OFF and ON. 4. Wait until acquisition (averaging) become >1000. 5. Press ‘Run/Stop’ button to stop acquisition, and press ‘Save as’.6. Save file as ‘.csv’.

Data analysis

Data analysis can be done semi-automatically by using a locally developed macro program on Igor Pro (cf. manual of elastic wave travel time analysis program). Regarding the data analysis, we need to consider acoustic impedance relation of this experiment. Since the acoustic impedance of the Copper backing reflector (ZCu=~45) is larger than that of the SiO2 glass sample (ZS=~12), the sample/backing reflector (R2) interfaces yielded a negative reflection coefficient (=(ZS-ZCu)/(ZS+ZCu)). Therefore, the R2 signal needs to be inverted to overlap with the R1 signal in phase. The macro ‘usfn()’ calculates elastic wave travel time after inverting the R2 signal before overlapping. There is another macro for conducting elastic wave travel time analysis without inverting the R2 signal.

ReferenceKono, Y., C. Park, T. Sakamaki, C. Kenney-Benson, G. Shen and Y. Wang, Review of Scientific Instruments

83, 033905-033908 (2012).

Figure 3

Training Course 4: Liquid/amorphous EDXD Data Analysis and Falling Sphere Viscometry Demonstration

Changyong Park

The data process of measured liquid/amorphous EDXD spectra consists of a few critical procedures including the primary beam estimation, the Compton background subtraction, and the structure factor normalization. The procedures are quite different from typical angle-dispersive diffraction data process, and there are several practical aspects by which the success of data analysis is affected. In this course, a set of amorphous EDXD data analysis and the pair distribution function analysis are exercised to understand those practical factors. Pre-measured EDXD data from SiO2 glass and Python-based all-in-one type data analysis software is provided to practice the analysis.

In the second part of training, Falling Sphere Viscometry is demonstrated with a captured video and ImageJ object tracker plugin application. With an example of FeS melt viscosity measurement, the practical factors involved in the experimental design are discussed. Training goals

1. Understand critical data reduction processes for liquid/amorphous EDXD data analysis and gain experiences with the issues involved in these analysis. 2. Explore the factors affecting liquid viscosity measurement with the Falling Sphere method.

Liquid/amorphous EDXD data reduction

The observed energy dispersive x-ray diffraction spectrum at a given 2θ angle can be described:

I m(2θ , E)=s (2θ) P (2θ ) A (2θ ,E )C (E ) I P (E)[I coh (2θ , E )+ I inc (2θ , E )] (1)

where, s(2θ) is a scale factor, P(2θ) ≈ cos2(2θ) the polarization factor for linearly polarized synchrotron beam in the horizontal plane, A(2θ,E) the x-ray attenuation, C(E) an energy dependent term (e.g., detector efficiency), IP(E) the primary white beam profile, Icoh(2θ,E) and Iinc(2θ,E) are the coherent and incoherent scattering from the sample, respectively. Practically, the polarization factor is a constant for the fixed angle and the angle dependence of x-ray attenuation is negligible for a cylindrical sample (i.e., A(2θ,E) A(E)). Thus, equation (1) can be effectively rewritten as:

I m(2θ , E)=s '(2θ)I P ,eff (E)[ I coh (2θ , E )+ I inc (2θ , E )] (2)

The scaled primary beam, s’(2θ)IP,eff(E), can be approximated by a non-linear least square fitting with Eq. (2) with respect to the highest 2θ angle data. Here, the unknown Icoh(2θ,E) is replaced with calculated < f 2(2θ,E) > for the best approximation of the primary beam, and

⟨ f 2 (2θ ,E ) ⟩=⟨ f 2 (q ) ⟩≡∑i

c i f i2(q) (3)

I inc (2θ , E )=I inc (q )≡∑i

c i I i ,Compton (q ) (4)

q= 4 π ∙ E12.3984

sin (θ) (5)

where, ci is the atomic fraction and fi(q) the atomic scattering factor of i-th element, respectively. The parameters to calculate f (q) and ICompton(q) are from International Tables for X-ray Crystallography [Ed. Ibers and Hamilton] and refs. [Cromer and Mann, 1967; Cromer, 1969], respectively.

The structure factor for liquid is defined as:

S (q )=I coh (q )−⟨ f 2 (q ) ⟩

⟨ f ( q ) ⟩2+1 (6)

where, ⟨ f (q ) ⟩ ≡∑i

c i f i(q). For each measured spectrum at different

2θ angles, a fragmented structure factor S(q) = S(2θ,E) can be obtained using the estimated IP,eff(E) as follows:

S (q )=S (2θ , E )=I m (2θ , E )−s ' (2θ ) I P,eff ( E ) [ ⟨ f 2(2θ , E)⟩+ I inc(2θ ,E)]

s' (2θ ) IP, eff (E ) ⟨ f (2θ ,E)⟩2+1 (7)

These fragmented structure factors are to be rescaled in reverse sequential order with respect to the one obtained at the highest-2θ, which oscillates around one by definition. An evenly spaced S(q) in q-space is obtained by error weighted spline-smoothening of the merged structure factor.

The error-bars are rigorously propagated from the counting statistics of raw data, assuming the counting probability follows the Poisson distribution (i.e., σ I=√I), and are convoluted with the uncertainty involved in the primary beam estimation. The increasing errors with increasing q arise from the effect of the atomic scattering factor for x-rays decaying with q and being further weighted with the shape of the primary beam profile. The required counting statistics to compensate this effect should be proportional to 1/ < f 2(q) >, which is impractical, therefore the practical limit of the S(qmax) is often chosen smaller than the instrumental limit (e.g., qmax = ~19 Å-1 at 2θ max = 34.9 ° and Emax = 65 keV for the primary beam estimation in this example). The maximum qmax defines the spatial resolution in real space, Δr = π/qmax, thus the limited qmax also limits the finest features that can be observed in the real space distribution of pair distribution function.

From an evenly spaced S(q), the reduced pair distribution function G(r) is obtained as:

G(r )= 2π ∫

qmin

qmax

q [S (q )−1 ]sin (qr )⋅ [ sin (q Δr)q Δr ]dq (8)

where,[ sin (q Δr)q Δr ] is the Lorch modification function to

implement the resolution broadening in real space. This modification function effectively removes the data truncation error in the Fourier transform.

ReferencesWaseda, Y., The Structure of Non-Crystalline Materials, McGraw-Hill, New York, 1980

Egami, T., 1978. Structural relaxation in amorphous Fe40Ni40P14 B6 studied by energy dispersive X-ray diffraction. Journal of Materials Science 13, 2587-2599.

International Tables for X-ray Crystallography, Ed. Ibers and HamiltonCromer, D.T., 1969. Compton Scattering Factors for Aspherical Free Atoms. The Journal of Chemical

Physics 50, 4857-4859.Cromer, D.T., Mann, J.B., 1967. Compton Scattering Factors for Spherically Symmetric Free Atoms. The

Journal of Chemical Physics 47, 1892-1893.

Falling sphere viscometry

Viscosity () of fluid can be calculated with the Stokes’ equation by using the terminal velocity of falling sphere () with correction factors for wall effect (F) [Faxén, 1922] and end effect (E) [Maude, 1961]:

η=gds

2 (ρ s−ρl )18ν

FE (1)

F=1−2 .104( ds

d l)+2 .09 ( ds

d l)3

−0.95( ds

d l)5

(2)

E=1+ 98

ds

2 Z+( 98 ds

2 Z )2

(3)

where and d are density and diameter, respectively, with subscripts s and l denoting the probing spheres and liquid, respectively. Z is the sample height.

In order to determine the viscosity precisely, measurements of diameter of the probing sphere (d s), density difference between the probing sphere and the liquid sample (s-l), and the falling-sphere terminal velocity () are important. The size of ball can be precisely measured by various means. The density of the sphere ball as a function of pressure can also be calculated by using a known equation of state (e.g., platinum, rhenium, and so on). However, it is difficult to measure liquid density in situ combined with the viscosity measurement. Fortunately, in reality, the uncertainty of liquid density can be minimized by adopting a sphere material having a significantly higher or lower density than the liquid density. For example, in the case of Pt sphere (21.45 g/cm 3 at ambient condition) in liquid NaCl sample (1.547 g/cm3 at ambient condition) [Kono et al., 2013], a 10% uncertainty in liquid density estimation will influence the viscosity estimation only by 0.8%.

The uncertainties in terminal velocity play a dominant role in the precision of the viscosity determination [Brizard et al., 2005]. Precision of terminal velocity measurement depends primarily on frame rate of the camera. Previous high-pressure viscosity measurements were conducted using limited imaging rates (typically from ~30-60 to 125 frames/second, or fps), which are suitable only for highly viscous materials such as silicate or oxide melts. Some studies report viscosities in the 4-20 mPa s range for iron alloy melts using falling sphere velocities determined based on only 2 – 4 images. This limited imaging rate makes it difficult to ensure that the falling sphere has reached terminal velocity and results in large uncertainties in the calculated viscosity. The high-speed camera (Photron FASTCAM SA3) that we are using these days can collect images at a rate of more than 1000 fps and is ideal for precise viscosity measurements on low viscosity materials [Kono et al., 2013].

The high-speed camera has a maximum image size of 1024 pixels in both horizontal and vertical and is located approximately 1.2 m downstream from the PE cell.

Variable pixel resolutions of 2.8-5.9 µm/pixel are available by using 5 or 10 times infinity-corrected objective lenses combined with lens tube lengths of 25-76 mm.

Figure 1 shows an example of falling W95Re5 sphere (126 µm in diameter) in liquid FeS recorded at 500 fps with an exposure time of 2 ms per frame.

The position of the W95Re5 sphere in each frame was analyzed by using the Tracker plugin in ImageJ software. The excellent linearity in the sphere travel distance and constant falling velocity with time indicates that terminal velocity was achieved (Fig. 2). Then, viscosity can be calculated with the Stokes’ equation (Eq. (1)).

It is important to monitor the motion of falling sphere with substantial oversampling in order to determine terminal velocity precisely. The high-speed camera plays an important role here. Low sampling rates of the falling sphere position may cause misinterpretation of terminal velocity, thus causing large uncertainties in the viscosity estimation.

ReferencesFaxén, H., 1922. Annalen der Physik 373, 89-119.Maude, A.D., 1961. British Journal of Applied Physics 12, 293.Brizard, M., Megharfi, M., Verdier, C., 2005. Metrologia 42, 298-303.Kono, Y., Kenney-Benson, C., Park, C., and Shen, G., Phys. Rev. B 87, 024302 (2013)

Figure 1

Figure 2