Ceramic micro-injection molded nozzles for
serial femtosecond crystallography sample
delivery
Cite as: Rev. Sci. Instrum. 86, 125104 (2015); https://doi.org/10.1063/1.4936843
Submitted: 04 May 2015 • Accepted: 16 November 2015 • Published Online: 08 December 2015
K. R. Beyerlein, L. Adriano,
M. Heymann, et al.
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Rev. Sci. Instrum. 86, 125104 (2015); https://doi.org/10.1063/1.4936843
© 2015 Author(s).
86, 125104
REVIEW OF SCIENTIFIC INSTRUMENTS 86, 125104 (2015)
Ceramic micro-injection molded nozzles for serial femtosecond
crystallography sample delivery
K. R. Beyerlein,1 L. Adriano,2 M. Heymann,1 R. Kirian,1,a) J. Knoška,3 F. Wilde,4
H. N. Chapman,1,3,5 and S. Bajt2,b)
1
Center for Free-Electron Laser Science, Deutsches Elektronen-Synchrotron, Notkestra βe 85,
22607 Hamburg, Germany
2
Photon Science, Deutsches Elektronen-Synchrotron, Notkestra βe 85, 22607 Hamburg, Germany
3
Department of Physics, University of Hamburg, Luruper Chaussee 149, 22607 Hamburg, Germany
4
Helmholtz-Zentrum Geesthacht, Max-Planck-Straße 1, 21502 Geesthacht, Germany
5
Centre for Ultrafast Imaging, Notkestra βe 85, 22607 Hamburg, Germany
(Received 4 May 2015; accepted 16 November 2015; published online 8 December 2015)
Serial femtosecond crystallography (SFX) using X-ray Free-Electron Lasers (XFELs) allows for
room temperature protein structure determination without evidence of conventional radiation damage.
In this method, a liquid suspension of protein microcrystals can be delivered to the X-ray beam
in vacuum as a micro-jet, which replenishes the crystals at a rate that exceeds the current XFEL
pulse repetition rate. Gas dynamic virtual nozzles produce the required micrometer-sized streams
by the focusing action of a coaxial sheath gas and have been shown to be effective for SFX
experiments. Here, we describe the design and characterization of such nozzles assembled from
ceramic micro-injection molded outer gas-focusing capillaries. Trends of the emitted jet diameter
and jet length as a function of supplied liquid and gas flow rates are measured by a fast imaging
system. The observed trends are explained by derived relationships considering choked gas flow
and liquid flow conservation. Finally, the performance of these nozzles in a SFX experiment is
presented, including an analysis of the observed background. C 2015 Author(s). All article content,
except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported
License. [http://dx.doi.org/10.1063/1.4936843]
I. INTRODUCTION
Serial femtosecond crystallography (SFX)1 uses femtosecond X-ray pulses produced by an X-ray Free-Electron
Laser (XFEL) to collect diffraction patterns from crystals to
study their internal molecular structure. The X-ray pulses
are intense enough to ionize a large proportion of the atoms
in the sample multiple times. The rapid ionization leads to
the formation of a plasma and the explosion of the sample.2
However, with a sufficiently short X-ray pulse, diffraction
patterns can be collected before the onset of significant atomic
motion. Depending on the intensity, pulses longer than about
30 fs cause structural disorder that is largely filtered out of the
data by the fact that only Bragg peaks are measured.3,4 This
method is opening new doors in structural biology, yielding
atomic resolution structures from micrometer-sized crystals
and smaller, radiation sensitive protein crystals,5–10 as well
as, enabling experiments to study fast structural protein dynamics.11–15 Considering the destructive nature of the pulses,
data collection is optimized by a serial approach, where a new
crystal is placed in the beam for each X-ray pulse. The Linac
Coherent Light Source (LCLS) FEL has the fastest repetition
rate of all currently operational hard X-ray FELs at 120 Hz,
but a much faster 4.5 MHz bunch mode will be implemented at
a)Current address: Department of Physics, Arizona State University, P.O. Box
871504, Tempe, Arizona 85287, USA.
b)Author to whom correspondence should be addressed. Electronic mail:
sasa.bajt@desy.de.
0034-6748/2015/86(12)/125104/11
the European XFEL, which is currently under construction in
Hamburg, Germany. Furthermore, as protein crystal samples
are precious, sensitive to solvation conditions and difficult
to produce, they should be delivered in their native growth
medium in such a way as to minimize their consumption.
Since the conception of the SFX technique, micro-jets
have been used for sample delivery, as the crystals can be
delivered in a fast, micrometer-sized stream of the crystallization buffer that is positioned to intersect the X-ray focus in
a vacuum environment. Early on, Rayleigh jets were found to
be ineffective, as they require high flow rates, form ice when
run in vacuum, and are prone to clogging with a suspension
of protein crystals.16 This led to the development of flowfocusing nozzles, which rely on a coaxial focusing gas to
produce the micrometer-diameter liquid jet.17,18
Early experimental and theoretical investigations of flowfocusing were carried out by the group of Gañán-Calvo.19–23 In
many of their studies, flow-focusing was achieved by drawing
air through a small orifice in a flat metal plate (flat-plate
apparatus), and forming a jet from a capillary precisely positioned above the orifice.24 The original apparatus was later
miniaturized, replacing the plate with a surrounding outer
borosilicate capillary that was flame polished at one end to
produce a smooth convergent aperture.17,18,21 This miniaturized design has been referred to as a gas dynamic virtual
nozzle (GDVN), and a general schematic of one is shown in
Figure 1. However, flame polished glass capillaries are fragile
and prone to considerable variability in their manufactured
geometry, including different diameters and straightness along
86, 125104-1
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Rev. Sci. Instrum. 86, 125104 (2015)
II. NOZZLE GEOMETRY INFLUENCE ON JET
CHARACTERISTICS
FIG. 1. Schematic of a gas dynamic virtual nozzle tip, identifying its various
parts and geometric parameters and showing how they are arranged in a
nozzle. The gas supply capillary is not shown in the drawing as it is normally
positioned far away from the tip. The drawing is not to scale, see the text
for details concerning nozzle dimensions. The gas aperture diameter is D g ,
the inner diameter of the liquid supply capillary is D l , the tip to aperture
distance is H , and the capillary tapering angle is θ c . The liquid is shown
in blue, flowing from left to right. In a SFX experiment, the X-ray beam
impinges the jet approximately at a right angle.
the convergent aperture, often resulting in a cross section that
does not have ideal axial symmetry.21 This can result in nonoptimal gas flow streams, causing decentering of the liquid
supply capillary relative to the gas aperture, and a different
optimum distance of the capillary orifice to the nozzle exit—all
of which have been shown to be important in the performance
of flow-focusing nozzles.20,21,23
To improve nozzle reproducibility while reducing fabrication complexity, we investigated ceramic micro-injection
molding to mass-produce high precision outer capillaries for
GDVNs. Micro-injection molding can fabricate items of varying length scales, including features with dimensions of a
few micrometers on parts which are centimeters in length.
The small micrometer-sized jets, which are desirable for the
SFX application, require the use of apertures in the range of
10-100 µm in diameter. During operation, stresses as high as
10 MPa can be applied to this aperture by the focusing gas.
Because of their high compression strength (50-500 MPa) and
elastic modulus (1-10 GPa), ceramics are suitable materials
for such applications. In addition to an increased mechanical
stability, ceramic micro-injection molded nozzles offer more
chemical stability than those produced from polydimethylsiloxane (PDMS) using soft-lithography25—enabling their use
with a wider range of solvents.
The present manuscript details the design, assembly, and
testing of our ceramic micro-injection molded nozzles and is
organized as follows. A brief review of the theory concerning
the relationship between the nozzle geometry and expected
performance is given as a motivation for our design. This is
followed by a detailed description of the nozzle design and
assembly. The jet characteristics resulting from this design and
their dependencies on the supplied liquid and gas flow rates
in a laboratory setup are demonstrated and discussed. Furthermore, experimental data obtained at an X-ray FEL using
our ceramic micro-injected nozzles are presented, focusing on
a discussion of the background levels from the nozzle. The
manuscript concludes with a summary of the results and ideas
for future utilization of ceramic nozzles.
The internal geometry of a GDVN determines the gas
and liquid flow regimes of a stable jet. When using GDVNs
to deliver precious protein samples in SFX experiments, one
of the most important parameters is the minimum liquid flow
rate, Qmin, as it determines the rate of sample consumption and
the smallest achievable jet diameter (further discussed in the
next paragraph). The study of Vega et al.23 found empirically
that the optimum minimum flow rate to produce a jet for low
viscosity fluids is given by the relationship
( ) 1/3
Dl
Qmin
µ/ρ,
(1)
= 2.5
Dg
Dg
where Dg and Dl are the gas aperture and liquid capillary
inner diameters, respectively, µ is the liquid viscosity, and ρ
is the liquid density. This minimum flow was obtained when
the liquid supply capillary was positioned a distance, H, away
from the gas aperture given by
( ) 1/4
H
Dl
.
(2)
= 0.6
Dg
Dg
When the capillary was positioned closer, the nozzle tended
to atomize the stream through a process called flow blurring.
At further distances, a higher liquid flow rate was necessary
to produce a stable jet. From Equations (1) and (2), it is also
evident that the geometric parameter that has the greatest effect
on the flow properties is the diameter of the gas aperture, Dg .
Later studies demonstrated that these relationships also hold
for convergent gas aperture nozzles19 and investigated scaling
relationships for high viscosity fluids.22 Although these empirical relationships were obtained for jets formed in air, they
form a basis for characterizing jets in vacuum as described in
Sec. IV.
Another important jet parameter to consider when designing nozzles for SFX experiments is the jet diameter. This is
linked to critical experimental quantities such as the sample
hit rate (fraction of X-ray pulses that hit a crystal), sample
consumption efficiency (fraction of crystals hit by an X-ray
pulse), and intensity of background signal from the protein
crystal solvent. The functional dependence of the jet diameter
on these quantities is found considering two cases: when the jet
diameter, D j , is either (1) larger or (2) smaller than the X-ray
beam diameter, Db . Considering a homogeneously dispersed
crystal solution, continuously flowing from a nozzle, the crystal hit rate, f h , is given by the product of the crystal concentration, ρc and irradiated volume, resulting in the respective
expressions for cases 1 and 2,
π
π
ρc Db2 D j , f h = ρc Db D 2j .
(3)
4
4
The sample consumption efficiency, f s , comes from the ratio
of the hit rate and the crystal flow rate, the latter given as the
product of the crystal concentration and liquid flow rate, Q l .
The liquid flow rate is related to the jet diameter and velocity,
v j , by
fh =
Ql =
π 2
D vj.
4 j
(4)
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Rev. Sci. Instrum. 86, 125104 (2015)
Using this expression, the sample efficiency is found to be
independent of crystal concentration, and given for the two
cases as
fs =
Db2 νXray
Db νXray
, fs =
,
Djvj
vj
(5)
where νXray denotes the X-ray pulse repetition rate. Finally,
the measured background from solvent scattering is proportional to the irradiated volume. This quantity is expressed in
Equation (3); therefore, the background increases linearly with
jet diameter for case 1, and quadratically for case 2.
Comparing these relations, it is clear that a smaller jet can
improve sample consumption efficiency and decrease background, with the tradeoff of reducing the hit rate for a constant
sample concentration. In some cases, the sample concentration
can be increased to make up for the loss in hit rate. However,
this strategy also has limits, as sample concentrations above
1010 crystals/ml that are often necessary for experiments have
been observed to cause jet instability. Nonetheless, the amount
of protein crystals that can be produced is often the limiting
factor in serial protein crystallography experiments. Therefore, a small jet is often desirable as it maximizes the number
of diffraction patterns collected from a given volume of sample
and improves the signal to noise by decreasing the background
in the patterns.
Designing a nozzle that produces small jets requires
understanding the fluid mechanics governing the jet formation
process. Gañán-Calvo24 has shown that the kinetic energy per
unit volume in a jet is equal to the pressure difference across
the nozzle aperture, ∆Pg , resulting in the relationship
∆Pg =
8ρl Q2l
π 2 D 4j
=
ρl v j2
2
.
(6)
Use of this relationship requires knowledge of the pressure
of the focusing gas inside the nozzle, which is dramatically
different than the pressure applied to the gas supply capillary,
due to the compressibility of gas. A more general relationship
in terms of the gas mass flow can be found by combining
Equation (6) with known relationships governing the flow of
compressible gasses through an aperture. For a given pressure
inside the nozzle, Pi , the mass flow rate of the gas is given
by
kmg
M
(7)
Q g = Pi A
k +1 ,
RT
k−1
1 + 2 M 2 2(k −1)
where A is the cross-sectional area of the gas aperture, R
denotes the ideal gas constant, T, the temperature, k = Cp /Cv ,
the ratio of specific heats of the gas, and mg , the molar mass
of the gas.26 The variable M denotes the Mach number of
the gas flow through the aperture and is defined as the gas
velocity divided by its speed of sound. The speed of sound
is the upper limit at which gas can pass through an aperture.
At this speed, the flow is said to be choked or critical. For
most gases, including helium, the flow of the gas through a
nozzle becomes choked when Pi /Po & 2, where again Pi is
the pressure inside the nozzle, and Po is the pressure outside
the nozzle. When this ratio is less than two, the Mach number
is given by the relationship26
1/2
( ) k −1
2
Pi k
,
(8)
− 1
M =
k − 1
Po
otherwise, for choked flow, M = 1. Then, from Equation (7),
we define the velocity
k +1
k−1
RT 1 + 2 M 2 2(k −1)
α=
,
(9)
kmg
M
and solving for the internal nozzle pressure, we obtain
Pi = αpg ,
(10)
where pg = Q g /A is the momentum of the gas flow through
the aperture per unit volume. For choked flow, Equation (9)
predicts a velocity of 1088 m/s for helium at STP, which
is approximately its speed of sound. Equation (10) can then
be used in Equation (6) in place of the internal nozzle pressure. Solving for the velocity of the jet results in the
relationship
2(αpg − Po )
.
(11)
vj =
ρl
When the pressure outside the nozzle is small with respect
to the pressure inside, the factor Po in this expression can be
disregarded. In this case, it becomes evident that the velocity of
the jet is proportional to the square root of the gas momentum
through the aperture and the gas mass flow rate. One can also
substitute Equation (10) into Equation (6) and solve for the jet
diameter, finding
41 1
8ρ
l
Q2.
(12)
D j = 2
π αpg − Po l
This expression suggests that the diameter of the jet will
get smaller with increasing gas flow, but is more strongly
dependent on the liquid flow.
In Section IV, measurements will be described to test the
trends in jet diameter and velocity predicted by Equations (11)
and (12). These tests are done in a vacuum of 10 Pa; therefore,
choked flow can be expected if the pressure inside the nozzle
exceeds 20 Pa. We are confident that it is actually above
100 kPa for all presented operating conditions because we have
observed gas flowing out of the nozzle when it is taken out
of vacuum and held at STP conditions: 300 K and 100 kPa.
The preceding equations can be utilized assuming a choked
gas flow, or M = 1. Furthermore, in the case of choked flow,
lowering the pressure outside of the nozzle beyond the critical pressure will not change the flow inside the nozzle, only
changing internal pressure can have an effect.26 Therefore,
the reported performance of the nozzle is expected to be the
same at lower chamber pressures, such as the conditions of the
measurements taken at LCLS presented in Section V.
III. NOZZLE DESIGN AND ASSEMBLY
The general scaling dependencies of Equations (1)
and (2) are helpful when designing a GDVN. From this
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Beyerlein et al.
Rev. Sci. Instrum. 86, 125104 (2015)
FIG. 2. The parts used to assemble the nozzle are depicted (a): (1) gas supply capillary, (2) liquid supply capillary, (3) ceramic injection molded outer capillary,
and (4) stainless-steel assembly tube. The inset of (a) shows a microscopic image of a laser-cut Kapton spacer before placement on a liquid capillary. Also
shown is an image of an assembled nozzle (b) with the tip indicated by a dashed box. A rendering of an x-ray tomogram of this tip shows details of the internal
geometry of a nozzle where the jet is formed (c). The nozzle components in this image are labeled in the same scheme as described for (a). Arrows indicate a
Kapton spacer visible in this image. The gas supply capillary is outside the view as it is typically positioned centimeters away from the gas aperture.
aforementioned theory and our experience in making nozzles
by the flame-polishing technique, an outer capillary suitable
for ceramic micro-injection molding was designed. The general shape of the designed outer capillary follows that depicted
in Figure 1, and images of an example outer capillary are
shown in Figure 2. A gas aperture diameter of Dg = 70 µm was
chosen to allow for the use of liquid supply capillaries with
inner diameters, Dl , from 10 to 75 µm. Using Equation (2),
our design was optimized for a tip-to-aperture distance of H
≈ 50 µm, which Equation (1) predicts will result in a minimum
flow rate around 10 µl/min. While this setup optimizes the
performance in terms of flow rate, as will be discussed later,
we have ultimately found out that a slightly larger distance
is more suitable for SFX experiments as it improves the jet
stability and straightness without dramatically changing the
flow rate for a jet. The tapering angle θ c of the capillary
was chosen to be 60◦ that is beyond the current maximum
collection angle of 45◦. The 500 µm inner diameter of the
ceramic outer capillary limited its maximum length to 16 mm
due to limitations of the molding process. A longer length
is desirable as it allows for easier interfacing and assembly
of the nozzle. An outer diameter of 1 mm was chosen to
match preexisting nozzle assembly tubes. The ceramic outer
capillaries were manufactured by Small Precision Tools (SPT,
Switzerland), using a mixture of corundum (Al2O3) and zirconia (ZnO2). The gas aperture of each ceramic capillary
was inspected with an optical microscope prior to its use
as a nozzle, and a mean gas aperture of 71.5 µm with a
standard deviation of 2.5 µm was measured from 20 delivered
pieces.
Our ceramic outer capillaries replaced the flame polished
glass capillaries when assembling GDVNs according to the
procedure described by DePonte et al.17 The parts of a nozzle
discussed in this paragraph are shown in Figure 2(a). For
the liquid supply, polymicro-fused silica capillaries with an
outer diameter of 352 ± 2 µm, measured by a scanning laser
micrometer (LaserLinc, Inc.), and inner diameters Dl of either
20, 30, 50, or 75 µm were used. Before assembly, the liquid
capillaries were sharpened to a point by wet mechanical
polishing with a half angle of 18◦. In some cases, the sharpened
tips were dipped into pure hydrofluoric acid (40%), for 15 s
to slightly etch the exposed glass and smooth the ground
surface. Then, two Kapton rings with an inner diameter of
350 µm and an outer diameter of 500 µm (hereafter referred
to as spacers) were placed on the liquid supply capillary to
coaxially align it with the outer capillary, as illustrated in
Figure 1. These rings were precision laser cut (LLT Applikation GmbH, Ilmenau, Germany) from a 100 µm thick Kapton
film (DuPont). Three legs were carved out of the outer edge
of the rings to allow gas to flow around them.27 A micrograph
of a spacer mounted in the Kapton film is shown in the inset
of Figure 2(a). Focusing gas was supplied to the GDVN by
a second polymicro-fused silica glass capillary of 100 µm
inner diameter inserted into the outer capillary through the
back of the assembly. The inner and outer capillaries could
be assembled and sealed together using either a screwedtogether nozzle holder16 or a stainless-steel metal tube of
1 mm inner and 1.58 mm outer diameter. Typically, liquid
and gas capillaries were around 2 m long. This length is
needed to connect our nozzles located inside the experiment
chamber to external sample reservoirs and injection system
using equipment like that at the Coherent X-ray Imaging (CXI)
instrument of the LCLS.18
After rough assembly, nozzle parts were carefully aligned
with a dedicated micrometer fiber alignment stage (Thorlabs,
Part No. MBT610D) before they were fixed in place. The stage
enabled precise positioning of the liquid capillary tip to the gas
aperture distance, H. Once the desired distance was achieved,
the gas and liquid capillaries were secured in place by gluing
them in the metal tube with two-component epoxy. A fully
assembled nozzle is shown in Figure 2(b). Assembled nozzles
were then tested for their performance as detailed in Sec. IV.
Poorly performing nozzles were easily recycled by burning the
epoxy away using a flame. Due to their high thermal stability,
the ceramic outer capillaries remained undamaged and could
be assembled into a new nozzle.
As our zirconia and alumina ceramic outer capillary is
not transparent and hence not compatible with optical microscopy, we used X-ray tomography to visualize the final internal
geometry of assembled nozzles. When seeing inside the nozzle
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Beyerlein et al.
Rev. Sci. Instrum. 86, 125104 (2015)
with visible light is critical, the piece can also be made with
translucent alumina. Figure 2(c) shows a rendering of an X-ray
tomogram of the tip of an assembled nozzle having a liquid
capillary inner diameter of 75 µm. A full tomogram of the tip
was recorded, which shows the full internal geometry of the
nozzle tip in three-dimensions. The tomogram was taken using a Phoenix Nanotom S instrument (General Electric Company) with an X-ray tube operating at 45 kV on a Mo target.
The tomogram was reconstructed from 2400 projections in a
360◦ rotation scan about the cylindrical axis of the nozzle. The
distance H for this nozzle was measured from the tomogram
to be 110 µm. The contrast in Figure 2(c) is good enough to
show small details such as the laser-cut Kapton spacer that is
visible at the bottom of the image. The rendering also clearly
shows that the tip of the liquid capillary has an uneven rim. This
feature was not intentional, but can happen during the nozzle
assembly process due to the fragility of the thin glass walls
that are formed. In Sec. IV, we will present the performance
of this nozzle, showing that it generally agrees with the derived
models for jet size and velocity. Therefore, it is believed that
this amount of rim unevenness results in a nozzle performance
that is still suitable for our experiments.
IV. CHARACTERIZATION OF NOZZLE
PERFORMANCE
The performance of GDVNs made with our ceramic outer
capillaries was assessed using the optical microscopy setup
depicted in Figure 3. hThe nozzles were tested in a chamber
with rough vacuum conditions to simulate a SFX experiment.
The chamber is made of a KF-40 aluminum nipple with two
side windows cut out and glass microscope slides glued over
the gaps. These windows enabled illumination and imaging of
the nozzle during the operation in the chamber. The chamber
was attached to an Edmunds XDS35 scroll pump, and an Oring seated on the back of the nozzle provided a sufficient seal
for the vacuum and was firm enough to hold the nozzle in place.
During the operation of a nozzle, typical chamber pressures
were in the range of 10 Pa, while the base pressure of the pump
was around 0.1 Pa.
Jet stability and breakup were imaged using a Photron
FASTCAM SA4 camera, which can take up to 500 000 frames
per second with a shutter speed of 1 microsecond. For 10 µm
droplets, this shutter speed allows for clear snapshot images of
the jet and droplets traveling at a speed of 10 m/s. The optics
consisted of a Navitar 12× Ultra-Zoom motorized lens and a
10× Mitutoyo objective lens, which allowed for a resolution
from 0.3 to 3 µm/pixel. Illumination was produced by a Karl
Storz xenon lamp coupled to a liquid light guide or a LDX
Optronics 250 mW multi-mode fiber coupled 635 nm laser
diode powered by a Newport LDP-3830 supply. The xenon
lamp provides a more uniform background, while the pulsed
laser source provides a faster time resolution. To image smaller
and faster droplets, we used the pulsed laser diode with a 500 ns
pulse duration (flat-top pulses), which allows clear imaging of
droplets at speeds up to 20 m/s. The image brightness was the
major factor limiting the pulse duration, and shorter pulses can
be used with a lower magnification to observe the stability of a
faster jet. A ground glass diffuser was placed between the laser
FIG. 3. The layout of the testing station used to characterize nozzles under
vacuum is shown in (a). Also depicted are a nozzle inserted into the vacuum
chamber and a close up of the objective lens and illumination optics (b).
In this image, the testing chamber is rotated 90◦ from its normal operating
orientation to show the windows and view through the chamber.
and the test chamber as needed to reduce the speckle from the
laser diode observed in the images.
Liquid was supplied to the nozzle by pressurizing a
polyether ether ketone (PEEK) cylinder filled with the liquid
sample. The pressurizing gas was controlled by a Parker
high-pressure self-relieving regulator installed upstream of
the reservoir. In the following tests, helium was used, but the
choice of gas used to pressurize the liquid reservoir is not
critical as nitrogen is also often used without an observed
change in the nozzle performance. Alternatively, we also
used a high-pressure liquid chromatography pump or a highpressure syringe pump to supply liquid to the nozzle resulting
in comparable nozzle performance. However, we have found
that the pressurized reservoir system offered the best flow
stability and sensitivity over a large range of flow rates. It
can be difficult to load fluids into syringe pumps without
gas bubbles. When this happens, it causes a slow response
time when changing the flow rate. The volumetric flow of
the liquid into the nozzle was measured with one of two flow
meters installed in series along the liquid line—the Sensirion
SLG64-0075 for 2-20 µl/min flow rates or the Sensirion SLI0430 for 5-80 µl/min flow rates. The precisions of these flow
meters were, respectively, measured to be 3% and 10% of the
measured flow rate, calibrated by weighing water collected
over a period of 30 min at different flow rates. During testing,
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Beyerlein et al.
a liquid pressure up to 10 MPa was typically applied to the
reservoir. The corresponding flow, Q l , through the nozzle then
depended on the inner diameter of the liquid capillary. While
both pressure and liquid flow were recorded, only flow through
the nozzle will be presented here as this is the conserved
quantity for an incompressible system, independent of the
tubing used upstream of the nozzle.
Helium gas was supplied to the nozzle in a similar way,
using a second Parker self-relieving pressure regulator connected to a Bronkhorst EL-Flow gas mass flow meter. Helium
was chosen as the focusing gas because it helps to minimize
X-ray background in two ways. First, background scattering
from the focusing gas is low, as helium does not scatter Xrays strongly. Second, its high speed of sound maximizes jet
speed, resulting in a thinner jet, and correspondingly reduced
background due to X-ray scatter from the water column. In
previous flow-focusing studies, the energy supplied by the
gas flow to the system was described in terms of the gas
pressure.19,23,28 However, we will base our analysis on mass
flow because this quantity is conserved throughout the nozzle,
regardless if the flow is choked at the exit gas aperture.
In the present study, a stability test consisted of inserting
a nozzle into the test chamber and observing the stability of
the jet for different liquid and gas flow rates. Nozzles were
first tested with water since it is the main solvent for most
protein crystal solutions. The stability test began by flowing
helium at a constant rate and then slowly increasing the liquid
flow starting from zero. After allowing a few seconds for
stabilization, the state of the jet was recorded. However, when
the gas pressure was changed, the liquid flow would be first
decreased to zero and then increased again in slow increments.
By always starting the liquid flow from zero, the possibility of
reporting erroneous jet stability due to well-known hysteresis
in the dripping to jetting transition in flow-focusing nozzles23
was reduced. The reported flow rates for the transitions are
then upper limits, as transition flow rates that are in some cases
as much as 5 µl/min lower can be obtained by starting from
a higher flow rate and slowly lowering the liquid flow rate.
However, in our experience, these states are only stable for
a few minutes and not always reproducible, so reporting the
upper limits of the transitions is more representative of the
long-term stability of the jet. While the specific behavior of
Rev. Sci. Instrum. 86, 125104 (2015)
the jet can be more complex, the state of the jet was classified
into three general categories as follows:
• Dripping: the meniscus is not stable, and drops are
quasi-periodically ejected from the nozzle.
• Jetting: a stable meniscus is present which is drawn into
a slender jet.
• Whipping: the jet stream is spatially unstable, and
“whips” around with an amplitude larger than its
diameter.
An example of a water jet stability phase diagram obtained
from the nozzle in Figure 2(c) is depicted in Figure 4(a).
Figure 4(b) shows example images of the nozzle and jet in
the various stability regimes taken with the pulsed laser illumination system. The stability behavior of the assembled nozzle
qualitatively agrees with other such diagrams presented elsewhere.19,29 However, a careful distinction must be made when
comparing our stability phase diagram to these results. In some
cases, the authors were primarily concerned with the stability
of the liquid meniscus, called local stability. Our study is
focused on the stability of an ejected liquid jet, often referred
to as global stability, as this characteristic is more important
for the application to SFX.
The phase diagram in Figure 4 shows that a jet is only
stable above a minimum liquid flow rate and up to a certain
maximum gas flow rate. For this particular nozzle, we determined that the jet was stable above a liquid flow rate of
12 µl/min and for a gas mass flow rate between 10 and
60 mg/min. At a gas flow rate above 60 mg/min, the jet became
spatially unstable (whipping). The growth of these whipping
oscillations along the length of the jet increased gradually
with increased gas flow. The transition to the whipping state
shown in Figure 4 was determined as the point where these
oscillations became comparable to the diameter of the jet.
Whipping has been postulated to be more prevalent in jets produced by nozzles constructed using tapered outer capillaries
than for flat-plate apparatuses.19 Nozzles for SFX applications
have a converging conical outer wall to minimize shadowing
of the measured diffraction pattern by clipping the diverging
scattered X-rays with the nozzle, which means a convergent
gas aperture is unavoidable even though it may be prone to
whipping. This whipping instability defines the upper limit of
FIG. 4. The experimentally obtained jet stability phase diagram (a) shows three distinct regimes for a nozzle flowing water with a liquid capillary inner diameter
of 75 µm. The gas mass flow rate and the pressure applied to the gas supply capillary are depicted. Also shown are example images of the jet (b) depicting a
dripping jet (left), a stable jet (center), and a whipping jet (right). The jet in these images is flowing from top to bottom.
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Rev. Sci. Instrum. 86, 125104 (2015)
FIG. 5. The measured jet diameter (black circles) and corresponding jet velocity (red squares) as a function of liquid flow rate (a) and gas mass flow rate (b) are
shown. The lines in these figures represent fits of the jet diameter assuming the dependence predicted by Equation (12). Also, the average measured jet length as
a function of liquid flow rate (black squares) and gas mass flow rate (red circles) is shown in (c). The error bars on gas and liquid flow rates show the precision
of the respective flow meters. The average value was obtained by averaging ten data points, so the standard errors of the measured flow rates are about three
times smaller than the error bars. Please refer to the text for a description of how jet diameter and jet length error bars are calculated. The nozzle used in these
experiments is the same as that depicted in Figure 2(c). All tests were performed with water. The measurements at different liquid flow rates were made with a
constant gas mass flow rate of 20 mg/min, while those for different gas flows were made with a constant liquid flow rate of 20 µl/min.
the gas flow that can be used with this type of nozzle in a SFX
experiment.
In the stable jetting regime, changing the liquid and gas
flow rates influences the jet diameter and length. The effects
of the liquid and gas flow on these parameters are depicted
in Figure 5. The same nozzle as that previously studied was
used for this test, and the reported diameters were measured
at a point on the jet 15 µm from the orifice. The zoom lens
position was set to achieve a pixel resolution of 0.3 µm/pixel
for images of smaller jets and 0.5 µm/pixel for those of larger
jets. As this resolution is close to the wavelength of light, the
jet appeared as two parallel black lines with grey borders. The
diameter was taken to be the average of the distance between
the black lines and the distance between the grey borders, and
the uncertainty was taken to be half the difference of these
values—roughly two pixels wide. The jet velocity was also
calculated from the measured jet diameters and liquid flow
rates using a reformulation of Equation (4),
v j = 4Q l /πD2j .
(13)
These data are also plotted in Figures 5(a) and 5(b) as a
function of the liquid and gas flow rates, respectively. The error
bars of the jet velocity are the uncertainties propagated from
the measured uncertainties of the jet diameter, which is the
dominant error.
Figure 5(a) shows that as the liquid flow rate was increased
between 10 and 60 µl/min with a constant gas flow rate, the
jet diameter was found to increase from 4 to 8 µm, and the
calculated jet velocity slightly decreased from 20 to 15 m/s. A
dependence following
fit of the jet diameter, assuming a Q1/2
l
the prediction of Equation (12), is also shown in Figure 5(a)
and is found to agree within the uncertainty of the measurement. Figure 5(b) shows that the jet diameter was also slightly
sensitive to the gas mass flow rate, as the diameter decreased
from 6 to 4 µm as the gas flow rate was increased between
5 and 35 mg/min, reflecting an increase in the average jet
velocity from 12 to 25 m/s. These observed velocities are in
fair agreement with those predicted by Equation (11) assuming
choked flow, as a helium gas flow rate of 20 mg/min through a
70 µm aperture is predicted to result in a 14 m/s jet, while 17
± 2 m/s was measured. A fit of the jet diameter trend assuming
the Q−1/4
dependence predicted by Equation (12) is also shown
g
in Figure 5(b) and seems to agree with the measured data.
Once the jet is formed, the jet length is governed by a
breakup process similar to the Plateau-Rayleigh instability.
The difference being that in the GDVN case, the focusing gas
changes the axial velocity gradient of the liquid in the jet.29
For experiments performed with X-ray beams, the jet length
is of importance as it determines the maximum distance of
the nozzle from the X-ray interaction region to intercept a
contiguous jet. Intercepting the jet before it breaks up into
droplets generally optimizes data collection efficiency, as will
be discussed later. The measured jet length for different liquid
and gas flows is shown in Figure 5(c). It was found that the
jet length fluctuated significantly for sequential frames in a
movie recorded at 30 000 frames per second. The values in
Figure 5(c) are then the average jet lengths found with the
error bars depicting the observed variation over a set of 100
sequential frames analyzed for each measurement condition.
Given a constant gas flow, it was found that, along with the
increase in jet diameter (Fig. 5(a)), an increase in the liquid
flow rate results in a longer jet. In this case, a longer jet is
explained by the longer time necessary for surface waves to
grow large enough to pinch off the stream into droplets due
to the increased jet diameter. Figure 5(c) also shows that the
jet length is largely unaffected by the gas flow rate. The same
behavior has also been observed for other nozzles tested with
the fast imaging system. As shown in Figure 5(b), a higher gas
flow results in a nearly two-fold increase in the jet speed and a
less than 20% decrease of its diameter. One would then expect
that such a jet would be about 50% longer, assuming a constant
surface wave growth rate. However, the observation that the jet
length is independent of the gas flow rate could be explained
by a surface wave growth rate that increases with the gas mass
flow rate, thus negating the effects of a faster jet.
The ceramic nozzle presented here shows typical behavior
and stability ranges that meet the requirements of most SFX
applications. We have assembled 180 nozzles with either a
50 µm or 75 µm inner diameter liquid capillary, of those 67%
(122 nozzles) made a suitable jet. Limiting to the case of
nozzles with 75 µm liquid capillaries that were ground with
an 18◦ angle, 73% (68 of 93) formed a jet. Further considering
those that were slightly etched with hydrofluoric acid, 13 out
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Beyerlein et al.
of 14 nozzles formed a suitable jet—suggesting a possible
route for further improvement of the nozzle stability. The
main observed difference between assembled nozzles is that
the produced jets are not perfectly coaxial with the nozzle,
but have different degrees of angular deviation. Most likely
this deviation indicates misalignment of the liquid capillary
with respect to the gas aperture and is caused by an insufficient precision in the spacer dimensions and positioning.
We found that the minimum liquid flow rate for a stable jet
can be shifted towards lower values (∼5 µl/min) by adjusting
the distance of the liquid capillary to the gas aperture, H.
This minimum flow rate is expected at the distance given by
Equation (2).23 However, we found that the stable jet regime
becomes narrower with respect to the gas flow rate at this
position compared with larger values of H. Also, when the
liquid capillary is closer, the transition to whipping is more
abrupt at a gas flow of around 30 mg/min. Finally, a smaller
H also leads to a higher sensitivity of the jet to the capillary
centering, resulting in an angular deviation of the jet as large
as 30◦. A plot of this angular deviation of the jet direction as a
function of the observed minimum water flow rate for a set of
different nozzles is shown in Figure 6. For our purposes, the
optimum liquid capillary to gas aperture distance, H, for a SFX
experiment is the smallest that leads to a straight and stable jet.
For the ceramic capillary size and geometry we tested (shown
in Figure 2), this distance is about twice the distance predicted
by Equation (2) (∼100 µm).
V. SAMPLE DELIVERY IN SFX EXPERIMENTS
In this section, we discuss the use of ceramic microinjected nozzles during a SFX experiment. In such experiments, the sample is delivered to the focused X-ray beam by
positioning the nozzle so that the liquid stream intersects the
X-ray focus with the flow running perpendicular to the X-ray
beam. The intersection is typically chosen in the continuous
jet of a stable jet rather than the breakup region because the
jet diameter is about half the average drop diameter—causing
FIG. 6. The observed jet angular deviation from a perfect coaxial alignment
is depicted for a set of assembled ceramic nozzles, which had different
minimum water flow rates to produce a stable jet. Each point in the plot
represents a different assembled nozzle from a set that was assembled with
H ranging from 20 to 200 micrometers. The higher recorded flow rates
correspond to nozzles assembled with a larger H , while those with lower
flow rates were assembled with a smaller H .
Rev. Sci. Instrum. 86, 125104 (2015)
half the background in the diffraction pattern due to X-ray
scattering from the liquid. Furthermore, unless the droplet
breakup is driven at a fixed frequency, the fraction of pulses
that hit the sample is reduced in the droplet region. Since
diffraction is recorded at high scattering angles, shadowing of
the diffraction by the nozzle is a concern. The conical outer
shape of the nozzle reduces the distance that the X-ray beam
must be placed from the nozzle tip to avoid shadowing of the
diffraction pattern. In our current design, the intersection point
must be at least 65 µm from the tip to avoid shadowing at
scattering angles below 30◦. However, even for distances from
the beam to the nozzle tip of 100 µm or more, high-angle X-ray
scattering from the nozzle is often observed originating from
a significant amount of X-ray intensity in the periphery of the
X-ray focus profile. GDVNs with a glass outer capillary16–18
add a diffuse background to X-ray diffraction patterns. In
contrast, our ceramic nozzles consist of a mixture of crystalline
ceramic phases and the background mainly consists of welldefined powder rings. Because ceramics strongly scatter high
energy X-rays, we studied the background produced in an
XFEL experiment to ensure that (i) the scattering will not cause
damage to detectors and hence limit the X-ray flux used during
the experiment and (ii) the collected data are not significantly
influenced.
An experiment was conducted at the CXI instrument of
LCLS using a focused 3 µm diameter X-ray beam at 6 keV.30
The nozzle was placed in the shroud system installed at CXI
which achieves a pressure of 0.01 Pa in the shroud and 10−5 Pa
in the main chamber when a gas-focusing nozzle is in operation.18 The nozzles used in the experiment performed the same
in this chamber as they did in the rough vacuum testing system
provided as part of the injector characterization lab (ICL) of
LCLS. Different nozzles with either ceramic injection molded
or glass flame-polished outer capillaries were used during the
course of the experiment. The tip of the nozzle was positioned
approximately 200 µm away from the X-ray focus, and flow
rates in the range of 40 to 60 µl/min were necessary to form a
long enough jet of the liquid suspension of protein microcrystals. The performance of the ceramic injection molded nozzles
was comparable to the glass nozzles with regard to flow rates
necessary for sample delivery. At one point during the experiment, a concentrated solution of lysozyme microcrystals31 was
flown in a ceramic nozzle producing a stable jet and yielding
13 000 diffraction patterns in just 13 min of data collection. A
summation of these images after local background subtraction
is shown in Figure 7(a). The signal from lysozyme is seen
to extend to about 3 Å, and little evidence of shadowing or
scattering from the ceramic nozzle is seen in the pattern.
During this experiment, it was observed that ice and other
substances had poor adhesion to the surface of the ceramic
nozzle. This allowed salt and protein debris that built up over
time to be cleaned off the tip of the nozzle. When a significant
amount of debris accumulated on the tip, we flushed the nozzle
with water, then reduced the gas flow to zero. Since the nozzle
was in vacuum, this caused ice formation at the tip, encapsulating the debris. Then by turning off the water and reinitiating the
gas flow, the blob of ice and debris was quickly blown away,
leaving a clean nozzle tip and a fully functional nozzle. If this
procedure was found to be insufficient (as when the nozzle was
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Beyerlein et al.
Rev. Sci. Instrum. 86, 125104 (2015)
FIG. 7. The sum of more than 13 000 lysozyme diffraction patterns collected with a ceramic nozzle is shown in (a). Also, the average diffraction pattern
backgrounds collected from glass (b) and ceramic (c) nozzles during an experiment at LCLS are compared. In each case, about 1000 patterns contributed to the
average. The radial average of the bottom half of these background patterns (d) compares the scattering signal coming from these nozzles.
completely clogged with the sample, preventing its flushing
with water), it was possible to clean the nozzle by removing
it from the vacuum chamber and rinsing it with a few drops
of water, or dipping the tip in an ultrasonic bath for a few
seconds. Similar cleaning procedures can be used for GDVNs
made with borosilicate glass outer capillaries, but the surface
adhesion of ice and other substances in vacuum was found to
be noticeably stronger.
Some of the experimental data were recorded when the
nozzle was dripping. These data were then sorted into water
hits and misses using the average intensity on a panel of the
detector where the scattering signal from water is at its peak.
Hits were the subset of collected diffraction patterns with a
non-zero intensity in this panel caused by a water droplet
intercepted by the X-ray beam, while misses were patterns
formed by X-rays which pass through the interaction region
without scattering from the sample stream. Figures 7(b) and
7(c) show averages of these misses taken from data collected
using a glass nozzle and a ceramic nozzle, respectively. The
observed signal in these patterns is attributed to the scattering
of unfocused X-rays from the nozzle tip, and as such is a
measure of the background signal coming from the nozzle.
Figure 7 shows then the contrast between the diffuse signal
from a nozzle with a glass outer capillary and the powder
rings from a ceramic outer capillary nozzle, attributed to the
corundum and zirconia phases. The powder rings from the
ceramic nozzle slightly decrease in intensity toward the top
of the diffraction pattern due to shadowing, as the nozzle was
placed into the interaction region from above.
The radial averages of the bottom half of the patterns in
Figures 7(b) and 7(c) are shown in Figure 7(d), comparing the
respective background level from each nozzle. The patterns
have not been rescaled and reflect the average detected intensity per pixel as a function of the scattering vector. They show
that the background from ceramic nozzles reaches a maximum
background level at the Bragg condition similar to that of a
glass nozzle. Therefore, data quality should not be affected by
the use of a ceramic nozzle any more than that from a glass
nozzle.
VI. SUMMARY AND DISCUSSION
We built and tested gas dynamic virtual nozzles made
from ceramic micro-injection molded outer capillaries. These
nozzles deliver predictable and stable jets reproducibly under
operating conditions compatible with SFX experiments. Such
a nozzle was assembled and characterized under various flow
conditions. A stable jet of water was formed with a helium gas
flow rate between 10 and 60 mg/min and a liquid flow rate
starting at 12 µl/min. At higher gas flow rates, a whipping
instability in the nozzle was observed, which is problematic
for the application to SFX experiments. The jet length and
diameter follow expected trends considering the geometrical
and physical relationships that govern choked gas flow and
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Beyerlein et al.
liquid flow conservation. No detrimental effects due to the
ceramic nozzles have been observed in XFEL experiments to
date.
In fact, the well-defined powder pattern from ceramic
nozzles could in some cases even be a benefit as opposed to
the higher diffuse background resulting from a glass nozzle.
For instance, if the signal from the sample is diffuse, as in the
case of solution scattering,12 the sharp rings from the ceramic
nozzle will produce a distinct background signal, which can
be masked or subtracted on a per image basis. Removal of the
diffuse ring background coming from a glass nozzle is more
complicated as it affects more pixels and overlaps with the
signal from the solution.
The feature resolution and reproducibility of microinjection molding allow for easier and faster manufacture of
nozzles producing micrometer-sized jets. Smaller, stable jets
at lower flow rates are within reach by further reducing the gas
aperture size and optimizing other nozzle design parameters.
Finally, ceramic micro-injection molded pieces may also be of
interest in other high-pressure sample delivery systems used
in SFX experiments, such as an injector for protein crystals
embedded in lipidic cubic phase.32
ACKNOWLEDGMENTS
We thank Harumi Nakatsutsumi (DESY) for assembling
and testing GDVNs and Dr. Dominik Oberthür (Univ. of Hamburg) for preparation of lysozyme crystal samples used during
XFEL experiments. The support of Andrej Berg and Lars
Gumprecht (DESY) in designing and Julia Maracke (DESY)
in fabricating the nozzle tomography adapter is acknowledged.
Tomographic measurements were carried out using an instrument of the P05 beamline in the Max von Laue Petra III experimental hall located at the Deutsches Elektronen-Sychrotron
research center (Hamburg, Germany). We thank Dr. Leonard
Chavas (DESY) for comments during drafting of the manuscript. Furthermore, the help and support of beamline scientists
at LCLS CXI is much appreciated. The LCLS experiment
was labeled LB32 and conducted in collaboration with the
groups of Professor John H. C. Spence (Arizona State University), Professor Michael F. Brown (University of Arizona),
and Professor Gebhard Schertler (Paul Scherrer Institute). The
authors also thank Dr. Uwe Weierstall, Professor John H. C.
Spence (Arizona State University), Dr. R. Bruce Doak (Max
Plank Institute for Medical Research), and Dr. Daniel DePonte
(SLAC) for many useful conversations related to designing and
operating GDVNs. We acknowledge support of the Helmholtz
Association through project oriented funds and the BMBF
through the Verbundforschung project 05E13GU1.
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