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How to Do the Cross Over Method for Compounds

How to Name Ionic Compounds

If you mix two compounds to form something new, then the new compound has a different chemical composition than the two original compounds. People can use the cross over method to determine formulas for ionic compounds. You need to use a valency table to tell you how many ions an element has and the positive or negative charge on the ions. Once you find the new compound's formula, you can determine what you've created. For example, when you combine sodium (Na) and chloride (Cl), you get NaCl, which is salt.

Look up the chemical symbol of the compounds you are using. You can use a periodic table, located in the references, to tell you the chemical symbol. For example, if you have sodium and oxygen, their chemical symbols are Na and O respectively.

Write out the chemical symbol for each compound being mixed. Use the valency table, located in the references, to find and write the valency of the compound next to its chemical symbol. A valency table lists compounds by there names or symbols. The valence tells you how many free ions the compound has. For example, if you are mixing sodium and oxygen, you would write Na +1, O -2. This means sodium has a valence of +1 and oxygen has a valence of -2.

Switch the valences numbers' places from its original compound to the other compound. This is where the cross over method gets its name because you are crossing over the valency numbers. Drop the positive or negative sign of the compound. In the example, Na 2, O 1, you switched the 2 from the O to the Na and the 1 from the Na to the O.

Eliminate the valency numbers you crossed over in the previous step, if any of these numbers are either the same or if the any of the numbers are one. In the example, you eliminate the 1 next to O, so the formula is Na2O, which is known as sodium oxide.

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About the Author

Carter McBride started writing in 2007 with CMBA's IP section. He has written for Bureau of National Affairs, Inc and various websites. He received a CALI Award for The Actual Impact of MasterCard's Initial Public Offering in 2008. McBride is an attorney with a Juris Doctor from Case Western Reserve University and a Master of Science in accounting from the University of Connecticut.

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About: Crossover experiment (chemistry)

In chemistry, a crossover experiment is a method used to study the mechanism of a chemical reaction. In a crossover experiment, two similar but distinguishable reactants simultaneously undergo a reaction as part of the same reaction mixture. The products formed will either correspond directly to one of the two reactants (non-crossover products) or will include components of both reactants (crossover products). The aim of a crossover experiment is to determine whether or not a reaction process involves a stage where the components of each reactant have an opportunity to exchange with each other.

12.6: Crossover Experiments

Chapter 1: understanding statistics, chapter 2: summarizing and visualizing data, chapter 3: measure of central tendency, chapter 4: measures of variation, chapter 5: measures of relative standing, chapter 6: probability distributions, chapter 7: estimates, chapter 8: distributions, chapter 9: hypothesis testing, chapter 10: analysis of variance, chapter 11: correlation and regression, chapter 12: statistics in practice.

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A crossover study design is also called a repeated measurements design, where experimental units receive all the treatments in different periods.

For instance, consider a clinical trial comparing drug A and drug B on 10 asthmatic patients randomly divided into group one, and group two.

First, each group receives different drugs for two weeks, recording their effect on the patient's physiology. This is followed by a washout period, to eliminate the drug from the patient's body.

Now, the groups are switched so that the second group receives drug A, and the first group receives drug B. This is termed a cross-over design. In this design, subjects act as their own controls, and their characteristics are not changed throughout the study. It also removes inter-subject variabilities.

This design is generally used in late-phase clinical trials involving drugs that help control the symptoms and not cure them completely.

For instance, in the previous example, drug B will not have an opportunity to demonstrate its effectiveness if drug A cures the patient during the first period.

Crossover experiments, also called the repeated-measurements design, is a study design in which all experimental units are exposed to all treatments in different periods. Crossover experiments are generally used in psychology, the pharmaceutical industry, agriculture, and medicine.

Crossover designs are performed even with smaller sample sizes since the samples can act as their controls. These are better than simple randomized trials since patients are exposed to all the treatments. Furthermore, cross-over designs are preferred to compare the bioavailability or ingestion of the drug in the human body and compare it with a reference drug. This method is unsuitable if the disease is chronic and stable and the drug should not completely cure the disease condition.

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Crossover trials: what are they and what are their advantages and limitations?

Posted on 7th September 2020 by Philip Heesen

Crossover trials are trials in which participants do not only receive one intervention, but multiple , and the effect of the interventions are measured on the same individuals . It is also described as participants receiving a sequence of interventions.

To make this concept less abstract, let us look at an example…

A researcher wants to compare the efficacy of the drug Valsartan with Iosartan, both given to treat high blood pressure. However, the researcher fears there might be a substantial risk of confounding (this beginner’s guide to confounding will help you understand this concept). In order to minimize this risk, she decides to make use of a crossover trial.

She recruits 120 participants into her study and randomly allocates them into 60 participants in group A and 60 participants in group B. At first, participants in group A will receive Valsartan for two weeks in order to treat their high blood pressure, and group B will receive Iosartan for a period of two weeks. After that, there will be a wash-out period of 4 weeks in which the study participants will not receive Iosartan or Valsartan. After that, group A will receive Iosartan for two weeks and group B will receive Valsartan for two weeks.

The researcher measures her primary outcome (reduction in mean blood pressure) twice: the first time after group A received Valsartan and a second time after group A received Iosartan.

This example easily explains the main steps that are followed during a crossover trial of the AB/BA type. The AB/BA model is the simplest type of crossover trial. At first, participants of one group will receive medication A and after a wash-out period, participants of the same group will receive medication B. The same applies to the second study group, but the other way around. Extensions to this form include the ABC/CBA/BCA regimens.

By using a crossover trial in order to compare several interventions, a researcher can minimize the risk of confounding because all interventions are measured on the same participants. One can say that study participants serve as their own control. This leads to another advantage which is less study participants are required compared to a standard parallel randomized controlled trial (RCT) . Reduction of sample size is consistent with the principle in medical research to use resources wisely. Furthermore, blinding of study participants can be maintained and statistical tests assuming randomization can be used .

Limitations

This design sounds very appealing, however there are various limitations that need to be considered:

• Crossover trials can only be conducted when the disease persists for a longer period of time, hence, crossover trials are mostly used in studying chronic diseases . There are some short-term illnesses or acute conditions that might be cured once they are treated and there are treatments that will have a permanent effect (i.e. surgery) on the patient. It is usually not possible to perform crossover trials in such cases.
• There is a great risk for aliasing. This term describes the risk that there might be a carry-over from the effect of the previous intervention on to the effect of the next intervention thereby altering results. Therefore, the treatment effect might not only be due to the treatment itself, but also due to interactions between treatment and study-period/sequence. Statistical tests have been suggested in order to test the carry-over risk, but a great chance of a type-II error (falsely accepting the null hypothesis, here: falsely accepting the hypothesis that there is no interaction between treatment and study-period or study-group) persists.
• It is difficult to estimate the time required in order for the intervention to be fully washed-out. While it might be relatively simple to estimate the wash-out period when the intervention is given as a drug looking at the half-life of the studied medications, things become a lot trickier when the interventions include psychological therapies, for example.
• In contrast to parallel designs, crossover trials consist of two study periods. This means that they usually take up more time , and statistical analysis can be more complicated if participants do not complete all stages of the trial.

Conclusions

In conclusion, crossover trials are a good study design that can be used to efficiently compare interventions on as few participants as possible when studying chronic diseases. However, many requirements (low risk of carry-over, wash-out period etc.) must be met and therefore it is not used as often as a parallel RCTs.

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Philip Heesen

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This is easy and best way to explain the concept

Excellent explaination !

In a rct cross over study ,two study group and one control group..what will be the design.and how the research question formed?

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Carryover Effects in Clinical Research

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If the effect of a treatment carries on after the treatment is withdrawn theft the response to a second treatment may well be due in part to the previous treatment. This, so called, carryover effect may bias any clinical trial in which subjects are tested more than once. Crossover studies can be routinely checked for this bias. In other study designs, however, common sense and alertness for unusual patterns in the data are the only defenses against it.

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What is crossover?

It is known that electroweak and QCD phase transitions in the standard model are so-called “crossovers” [1]. What is the difference between a crossover and a phase transition of the second kind?

[1] See eg., Sticlet, D. “Phase Transitions in the Early Universe. Electroweak and QCD Phase Transitions” [ PDF ].

• quantum-field-theory
• terminology
• phase-transition

• 2 $\begingroup$ You may also find it interesting to look up the BEC-BCS crossover for clouds of cold interacting fermionic atoms. $\endgroup$ –  Emilio Pisanty Commented Jul 19, 2015 at 12:21
• $\begingroup$ This answer provides a short definition and a relevant reference. $\endgroup$ –  xebtl Commented May 25, 2016 at 13:05
• $\begingroup$ … though be it said that I do not agree with the dismissive tone of the answer I linked :-) $\endgroup$ –  xebtl Commented May 25, 2016 at 13:14
• 1 $\begingroup$ Related/possible duplicate: physics.stackexchange.com/q/8879 $\endgroup$ –  valerio Commented Mar 1, 2018 at 17:14

2 Answers 2

As a handwaving definition, “crossover” is a generic term to describe a smooth transition between two separate phases of matter, upon changing some (thermal/non-thermal) parametres.

Well-known examples in strongly-correlated condensed matter are BEC-BCS crossover and the Kondo effect. In ultracold Fermi gases, a BEC-BCS crossover occurs by tuning the interaction strength, where the system “crosses over” from a Bose-Einstein-condensed (BEC) state to a Bardeen-Cooper-Schrieffer (BCS) state without encountering a phase transition . In certain metallic compounds with a dilute concentration of magnetic impurities, the Kondo effect occurs when the temperature is reduced below a certain threshold, and the system “crosses over” from a normal Fermi liquid phase ( weakly -coupled to impurities) to a “local” Fermi-liquid phase where conduction electrons form strongly -bound spin-singlets with the impurity electrons, without any phase transition involved.

The key point is that in a crossover, no canonical “phase transition” occurs, although there is a drastic change in the phase of the system. Remember that “phase transitions” are defined à la Ehrenfest (discontinuities in the derivatives of the Free energy functional) or à la Landau (symmetry-breaking mechanisms). A crossover is thus not associated with a change of symmetry, or a discontinuity in the free energy functional. Typically, it occurs in a region of the phase diagram, rather than a singular point.

Microscopically, in a crossover, the ground-state of the system changes radically (so that any perturbative expansion around the original ground-state will fail to capture the new ground-state), but in a very smooth manner; ie., without any discontinuity in the thermodynamic observables (which is the hallmark of phase transitions).

Beyond that handwaving description above, if we define a phase as a fixed-point for the renormalization-group (RG) flow [see eg. Ref. 1], then we arrive at a more precise definition for a crossover . Crossover happens when more than one critical fixed-point appear in the phase diagram [Ref. 2, sec. 3.11 ]. In such cases, the phase of the system depends on several relevant parametres (in the RG sense). The criticality is therefore richer: Tuning these parametres leads to different types of criticality (or universality classes).

Ref. 2 provides a simple instance of crossover for a Heisenberg model with a uniaxial anisotropy:

$$ H = -J \sum_{\langle i ,j \rangle} \mathbf{S}_i \cdot \mathbf{S}_j - D \sum_i (S_i^z)^2 $$

The figure shows critical behavior of the Heisenberg universality type for $ D = 0 $. At high temperatures, the system is in a paramagnetic (disordered) phase, and as one lowers the temperature (below $T_c$) the system orders.

For a finite $D$, when $ D > 0 $, the critical behaviour of the anisotropic Heisenberg model is governed by an Ising-type fixed-point (marked with ‘I’ in the figure), while its critical behavior for $ D < 0 $ is determined by an XY-type fixed-point. These are two radically different phases (and universality classes), and correspond to disparate ground-states. This indicates also that the Heisenberg fixed-point with $ D = 0 $ has two relevant variables, $ t \propto T − T_c $ and $D$ (besides the external field).

Therefore at $ D = 0 , T = T_c $, we will observe a “crossover” phenomenon.

[1] Pacciani, L. (ed). “Statistical Mechanics”, WikiToLearn, sec. “ The Renormalization Group ”.

[2] Nishimori, H. and G. Ortiz, “Elements of Phase Transitions and Critical Phenomena” (2010) [ wcat ].

• $\begingroup$ Different phases have different symmetries. During phase transitions, some of these symmetries are broken (or restored), as in spontaneous symmetry breaking. During crossover, these symmetries should change somehow. Right? Am I wrong or don't understand what you mean by the phrase "A crossover is thus not associated with a change of symmetry" $\endgroup$ –  maynak Commented Jul 21, 2018 at 13:32
• $\begingroup$ @maynak: I meant that a crossover is not necessarily accompanied by a spontaneous symmetry breaking. For example, occurrence of the Kondo effect (mentioned above) does not break any symmetries of the Fermi liquid, although the ground-state properties change drastically. So, it is not always true that “during crossover, ... symmetries should change somehow”. $\endgroup$ –  AlQuemist Commented Jul 26, 2018 at 11:52
• $\begingroup$ In this picture is $D=0$,$T=T_c$ a fixed point? If yes are crossovers always at (or maybe more accurately near) fixed points? Is the point that near the crossover there is a transition where the flow will either go near the Ising, if on one side, or near the XY model, if on the other? And that this will show a transition in critical behavior. $\endgroup$ –  Kvothe Commented May 22, 2020 at 15:37

There is no universally accepted definition of "crossover", so no answer is objectively correct, but I've usually heard the term used in a slightly different way than what AlQuemist describes. AlQuemist seems to be describing a Kosterlitz-Thouless transition, at which the free energy density is smooth but non-analytic (so that a perturbative expansion from one phase cannot reach the other phase). While very difficult to detect experimentally or numerically, KT transitions are still "sharp" in the sense that the points of non-analyticity form lower-dimensional submanifolds of parameter space. If you define a phase to be a maximal analytic connected region in parameter space, then a KT transition is still a true phase transition, although a somewhat nonstandard one because the free energy density remains smooth.

I've heard the term "crossover" to describe something different - a qualitative change in the nature of a state within the same phase . If two points of the phase diagram are well-separated, then the corresponding states can appear qualitatively different even though they're in the same phase (and therefore have identical symmetries, extreme IR behavior, etc.). One way to make this semi-precise is if there are two different correlation functions $C_\varphi(x - y) := \langle \varphi(x) \varphi(y) \rangle$ and $C_\psi(x - y) := \langle \psi(x) \psi(y) \rangle$ whose correlation lengths (or decay exponents, in the case of quasi-long-range order) cross each other within a phase. Roughly speaking, the "most important" observable in a state is the one with the longest correlation length (or slowest decay exponent), so at this kind of crossover, the "most important" observable for describing the state's behavior changes. Nevertheless, everything remains analytic so there's no sharp qualitative change in the state's behavior - clearly there will be a region within the phase where both correlation functions have similar correlation lengths/decay exponents, and so are roughly equally important for describing the state's long-distance behavior.

• $\begingroup$ Interesting definition of "crossover". But let me remind you that I did not mean BKT (or infinite order phase transitions) in my answer. Notice the two examples, esp. the Kondo effect. $\endgroup$ –  AlQuemist Commented Mar 1, 2018 at 16:36
• $\begingroup$ I think “phases” are best (& most precisely) described in a renormalization-group (RG) sense: The fixed-points of the RG flow. In this sense, you cannot have a “ qualitative change in the nature of a state within the same phase” — afaiu. A qualitative change in the phase implies a drastic change in the nature of the ground-state; otherwise, changes would be very “incremental”/perturbative. $\endgroup$ –  AlQuemist Commented Mar 1, 2018 at 16:39
• $\begingroup$ @AlQuemist Interesting - it seems we are using two different definitions of "phase" and "phase transition". You are defining a phase as a basin of attraction for an RG fixed point, while I am defining it as a maximal analytic domain for the free energy in parameter space. Under my definition, two different phases are by definition necessarily separated by a phase transition (at which the free-energy density is non-analytic). I thought that the definitions were equivalent, but I don't know of a proof. $\endgroup$ –  tparker Commented Mar 1, 2018 at 18:14
• 1 $\begingroup$ @RyanThorngren My understanding is that the order of the Higgs transition depends on the value of the Higgs mass $m_H$; it is first-order for $m_H < 75 \text{ GeV}$, but the transition line terminates at a multicritical second-order transition around $m_H = 75 \text{ GeV}$. The Higgs transition was indeed believed to be first-order until around 1998, when the LEP collider ruled out a light Higgs. See physics.stackexchange.com/questions/367398/… for more details. $\endgroup$ –  tparker Commented Mar 2, 2018 at 0:07
• 1 $\begingroup$ @SRS Yes, it can: en.wikipedia.org/wiki/Non-analytic_smooth_function . $\endgroup$ –  tparker Commented Jan 4, 2020 at 23:01

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• What was the first game to intentionally use letterboxing to indicate a cutscene?
• How to bid a very strong hand with values in only 2 suits?
• How is Victor Timely a variant of He Who Remains in the 19th century?