Lecture 5: X-ray measurement techniques

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1 Lecture 5: X-ray measurement techniques Contents 1 Introduction 1 2 Powder photographs Debye-Scherrer method Focussing method Pinhole photographs X-ray diffractometers 6 4 X-ray detectors Proportional counters Geiger counters Scintillation counters Semiconductor counter Introduction Practical methods of measuring/recording x-ray diffraction patterns are divided into two broad categories 1. Powder photographs 2. X-ray diffractometers Powder photographs make use of cameras to record x-ray diffraction patterns. These cameras can be of the analog type (film camera) or more often now are of the the digital variety using charge coupled devices (CCDs) to record x-ray diffraction patterns. The advantage of the camera technique that it is a single shot instrument i.e. all the diffraction lines are captured simultaneously. This 1

2 Figure 1: The geometry of the Debye-Scherrer method with the sample at the center of the circle and the film around it. Taken from Elements of X-ray diffraction - B.D. Cullity. is advantages when the stability of the x-ray source is questionable (very rare!) or more frequently when x-rays are used to study dynamic systems where time is of essence. Intensity measurements in camera techniques are not very reliable though and when relative x-ray intensities are important X- ray diffractometers are used. In x-ray diffractometer the detector is scanned over a 2θ range and the intensities are recorded at each angle to get a plot of Intensity vs. 2θ. 2 Powder photographs Powder photographs can be further divided into three methods depending on the relative positions of the source, sample, and detector. 2.1 Debye-Scherrer method In this method the sample is placed at the center of a cylinder and the film is wrapped around it. The geometry of the Debye-Scherrer method is shown in figure 1 and a camera is shown in figure 2. The sample in the middle can be rotated, for single crystal samples. There is also an opening for the incident beam and beam stop to cover the primary beam (forward scattered beam), as shown in figure 3. Diffraction lines are seen in the Debye-Scherrer method as lines around the center primary beam spot. The distance of the lines from the center spot, the value S in figure 1, gives the d-spacing of the plane corresponding to that 2

3 MM3030: Materials Characterisation Figure 2: Debye-Scherrer camera with the cover plate removed. Taken from Elements of X-ray diffraction - B.D. Cullity. Figure 3: The collimator for the primary beam and the beam stop in DebyeScherrer method. Taken from Elements of X-ray diffraction - B.D. Cullity. 3

4 Figure 4: Geometry of the focussing camera. Taken from Elements of X-ray diffraction - B.D. Cullity. line. The resolution of the Debye-Scherrer method depends on the radius of the cylinder around the sample. Resolving power is defined as the ability to resolve two closely spaced diffraction lines - close d-spacing or 2θ. The resolving power in d-spacing can be written as d d = S cotθ (1) 2R where R is the radius of the cylinder. Thus, higher the value of R smaller the d that can be resolved. The issue with having a larger cylinder is that the diffracted x-ray intensity goes down as distance from the sample to the film increases. This is because of scattering of the x-rays by the atmosphere. Thus, a larger exposure time is needed for larger cylinder sizes. This tradeoff determines the optimum camera size in the Debye-Scherrer camera. 2.2 Focussing method In the focussing method, the sample, source, and film (detector) are placed on the surface of the cylinder. The geometry of the focussing camera is shown in figure 4. X-rays diffracted by same (hkl) planes from points A and B, which are spatially separated on the sample, converge to the same point F on the detector. The angle α is equal to π 2θ. Thus, all rays from the source that fall on the sample and get diffracted by the same angle will 4

5 Figure 5: The Seeman-Bohlin focussing camera. X-ray diffraction - B.D. Cullity. Taken from Elements of focus on the same spot on the film. The Seeman-Bohlin camera is based on the focussing technique, shown in figure 5. The x-rays from the source pass through a collimator and fall on the sample. These get diffracted at different angles depending on the (hkl) plane and diffracted x-rays from planes with the same d-spacing converge on a spot in the film. The resolving powder of the Seeman-Bohlim camera is given by d d = U cotθ (2) 4R where U is the distance of the diffraction spot in the film from the origin, refer figure 5 and R is the radius of the cylinder. By comparing to equation 1 it is seen that the resolving power of the Seeman-Bohlin camera is higher than the Debye-Scherrer camera. 2.3 Pinhole photographs A flat film is used in this, placed at a suitable distance from a polycrystalline sample. Monochromatic x-rays fall on the sample, which is perpendicular to the incident x-rays. The arrangement in pinhole photographs is shown in figure 6. The advantage of the pinhole arrangement is that the full Debye ring pattern is captured unlike the other two techniques where only a portion of the ring pattern (that intersects with the film) is captured. The disadvantage is that only a small θ range is captured, either the low angle or the high angle (in back reflection) end. The pinhole photograph can be used either 5

6 Figure 6: Pinhole camera arrangement. Taken from Elements of X-ray diffraction - B.D. Cullity. in forward or backward reflection mode. In either, the Bragg angle can be calculated by knowing the radius of the Debye ring, U and the distance of the film from the source, D. tan2θ = U 2D F orward tan(π 2θ) = U (3) 2D Backward The advantage of the pinhole camera is that large polycrystalline samples can be examined - where the grain size is large so that a proper ring pattern cannot be obtained. In such samples, the other two methods might not be able to capture the ring pattern. By collecting the full Debye pattern in pinhole photographs this problem is avoided. 3 X-ray diffractometers For most applications, x-ray diffractometers have replaced powder photographs. In a diffractometer the intensity of the x-rays is converted directly into an electronic counter - typically a current pulse. The design is similar to a Debye-Scherrer camera, with the source and detector located on the surface of a cylinder with the sample at the center. The source sweeps a certain θ 6

7 Figure 7: Schematic of the X-ray diffractometer. Taken from Elements of X-ray diffraction - B.D. Cullity. range specified by the operator and the detector moves over the 2θ range. At each 2θ value the intensity is recorded by the detector to give a plot of I vs. 2θ. The schematic of the x-ray diffractometer is shown in figure 7 The measurement of intensity can be done in two modes 1. Continuous - In this the counter (detector) travels at a constant angular speed and the intensity is measured. The angular resolution then depends on the type of detector and determines the maximum travel velocity. 2. Intermittent - Here the counter stops at a given 2θ value, records the intensity, moves to the next angle and measures and so on. Intermittent mode is typically slower than the continuous mode but offer significantly higher signal/noise ratios which are useful especially for small volumes. The resolution is operator dependent since it depends on the step size specified at the beginning of the scan. The important criteria in the diffractometer is that the source needs to be stable during the entire operation range especially for accurate measurement of intensity. Some single crystal studies can take close to 24 hours for compilation of data. Hence we need sources that can be stable over these long 7

8 Figure 8: Linear range and saturation of the different types of x-ray detectors. Taken from Elements of X-ray diffraction - B.D. Cullity. operation times. Most polycrystalline metallurgical samples can be scanned within an hour. 4 X-ray detectors X-ray detectors (counters) are similar in principle in counters used for measuring radioactive particles. The basic principle is in converting the incoming radiation (x-rays, γ-rays, α-particles) into current pulses with the current directly proportional to the intensity of the incoming radiation. Sensitivity and resolving time are two key issues when choosing x-ray counters. We want a linear relation between the quanta absorbed and the detector. When saturation happens the linear relation breaks down so that an increase in quanta absorbed no longer leads to a linear increase in the quanta detected. This regime is also called counting loss regime. The linear range depends on the type of detector and is shown in figure 8. The resolving time is defined as the time between two successive pulses that can be detected. If the pulse before the resolving time then we will be in the counting loss regime since the quanta produced by the new pulse will add to the quanta from the first pulse. The resolving time determines the speed of the instrument. There are 8

9 Figure 9: Gas based x-ray counter - proportional or Geiger. Elements of X-ray diffraction - B.D. Cullity. Taken from four types of counters depending on how the current is produced 4.1 Proportional counters This is a gas based counter similar to the Geiger counter. The schematic of the counter is shown in figure 9. The schematic and working principle is the same for the proportional and the Geiger counter. The x-rays fall on the gas and ionizes it. The gas used is typically a rare gas like Xe, Ar, or Kr. The electrons produced by ionization are accelerated towards the wire anode at the center and produce a current. Also, accelerated electrons can hit other ions and produce further ionization, leading to amplification (which depends on the voltage difference between the cathode and anode). The current is thus proportional to the number of electrons produced by ionization which is proportional to the incoming x-ray intensity. The proportional counter is a fast counter and linear up to approximately 10 4 cps (counts per second). The amplification factor in the proportional counter is typically between but a reasonable intensity of incident radiation is needed for detection. 4.2 Geiger counters Figure 10 shows the effect of the applied voltage (between the wire anode and the cathode) on the amplification factor of a gas counter. The difference between the proportional and Geiger counter is the applied voltage in the Geiger counter is higher. The higher voltage means that electrons get accelerated to the anode while the ions also get accelerated to the cathode. 9

10 Figure 10: Gas based x-ray counter - amplification vs. applied voltage. Taken from Elements of X-ray diffraction - B.D. Cullity. This difference is shown schematically in figure 11. The accelerated electrons and ions can also interact with other neutral ions producing an avalanche. Typical amplification factors in the Geiger counter can be as high as Thus, a small signal can be amplified easily. But the Geiger counter is slow since the ions need to be neutralised before the arrival of the next signal. Using figure 8 it can be seen that the Geiger counter reaches saturation earlier than the proportional counter. The other name for the Geiger counter is the Geiger-Müller counter which is used for detecting ionizing radiation. 4.3 Scintillation counters Proportional and Geiger counters are both gas based counters and were historically used as X-ray detectors. Scintillation counters are the newer detectors and it is a solid state detector. The schematic of the scintillation counter is shown in figure 12 The detector consists of a sodium iodide (NaI) crystal doped with thallium that is capable of converting the incident x-rays to blue light. The x-rays raises the electron from the valence shell to the conduction shell of the NaI crystal and when this electron falls back to the valence shell it emits visible radiation (x-ray fluorescence). The visible radiation produced then falls on a photomultiplier tube (PMT) which converts it to electrons, which can be detected. The current produced is directly related to the intensity of the x-ray fluorescence which is related to the intensity of the incident 10

11 Figure 11: Gas based x-ray counter - proportional vs. Geiger. Taken from Elements of X-ray diffraction - B.D. Cullity. Figure 12: Schematic of the scintillation counter. Taken from Elements of X-ray diffraction - B.D. Cullity. 11

12 radiation. 4.4 Semiconductor counter This is newest form of x-ray detector and is also an example of solid state detector. It uses an intrinsic semiconductor with no excess electron or hole carriers. X-rays incident on the semiconductor produces electron-hole pairs which are separated by applied bias and detected as current. The current is proportional to the incident x-ray intensity. Semiconductor counters are extremely fast but require cooling (lq N 2 ) to minimize thermal electrons that are a source of noise in the detector. We will see semiconductor detectors later in the context of energy dispersive detectors for the TEM. 12

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